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Artificial neural network modeling of O2 separation from air in a hollow fiber membrane module.

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ASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING
Asia-Pac. J. Chem. Eng. 2008; 3: 357–363
Published online in Wiley InterScience
(www.interscience.wiley.com) DOI:10.1002/apj.155
Research Article
Artificial neural network modeling of O2 separation
from air in a hollow fiber membrane module
S. S. Madaeni,* G. Zahedi and M. Aminnejad
Department of Chemical Engineering, Razi University, Kermanshah, Iran
Received 30 October 2007; Revised 21 February 2008; Accepted 18 April 2008
ABSTRACT: In this study artificial neural network (ANN) modeling of a hollow fiber membrane module for separation
of oxygen from air was conducted. Feed rates, transmembrane pressure, membrane surface area, and membrane
permeability for the present constituents in the feed were network input data. Output data were rate of permeate
from the membrane, the amount of N2 in the remaining flow, and the amount of O2 in the permeate flow. Experimental
data were obtained from software developed by Research Institute of Petroleum Industry (RIPI). A part of the data
generated by this software was confirmed by experimental results available in literature. Two third of the data were
employed for training ANNs. Based on different training algorithms, radial basis function (RBF) was found as the best
network with minimum training error. Generalization capability of best RBF networks was checked by one third of
unseen data. The network was able to properly predict new data that incorporate excellent performance of the network.
The developed model can be used for optimization and online control.  2008 Curtin University of Technology and
John Wiley & Sons, Ltd.
KEYWORDS: hollow fiber membrane; artificial neural networks; simulation
INTRODUCTION
Membrane-based gas separation is an important unit
operation for the separation of gas mixture in oil, petrochemical and gas industries, separation of air into high
purity nitrogen and oxygen-enriched air, and removal
of acid gases such as CO2 and H2 S from natural gas,
and of organic vapors from air.[1] Membrane technology often offers cheaper capital and utility costs and has
displaced conventional separation techniques in many
areas. The increasing market for membrane technology has motivated interest in development of reliable
design strategies that aim to optimize the performance
of membrane separation systems. To achieve a desired
separation, a large membrane area is often required in an
industrial plant. This area is supplied in a modular configuration, for which there are a number of variations.
Historically, plate and frame modules have been used,
but more recently, spiral-wound and hollow fiber modules have attracted a lot of interest as these offer much
higher packing densities.[2] Since area per unit volume
of hollow fiber modules is very large, they have many
applications in gas industries. To minimize the technical risk in the design of any new process or to optimize
*Correspondence to: S. S. Madaeni, Department of Chemical
Engineering, Razi University, Kermanshah, Iran.
E-mail: smadaeni@yahoo.com
 2008 Curtin University of Technology and John Wiley & Sons, Ltd.
operation parameters, development of an accurate process model is essential to describe the process behavior.
This is particularly important for membrane systems
which are usually competing with well-understood traditional separation techniques. For membrane technology, it is necessary to understand the process for a
reliable design in order to avoid the need for time and
cost consuming experimental and pilot studies.[3,4]
Gas separation process by membrane is a nonlinear
system with multiple variables, large time delay, strong
coupling, and severe uncertainty.[5] So applying traditional procedures to model a membrane can cause some
problems such as:
1. Despite the fact that some processes have been in
practice for many years, their mechanisms are still
not understood, e.g. reactive membranes.
2. A large number of reactions and intermediates play
significant roles in reaction systems.
3. In many cases, modeling depends on hidden state
variables, such as adsorbed surface components
whose concentrations cannot be quantified using
conventional measurement techniques.
4. Use of unique global mass rate law may not be
possible because the rate determining steps may
change with varying operating conditions.
Applying artificial neural network (ANN) for modeling can render prementioned problems. Various studies
358
S. S. MADAENI, G. ZAHEDI AND M. AMINNEJAD
Asia-Pacific Journal of Chemical Engineering
have been carried out on ANN modeling in chemical
engineering.[6,7] Based on our literature survey, there
was no attempt on ANN modeling of hollow fiber membrane for gas separation.
ARTIFICIAL NEURAL NETWORKS
Neural networks (NNs) are models inspired by the
structure and the functions of biological neurons. A
network is composed of units or nodes that represent
the neuron bodies. The units are interconnected by links
that act like axons and dendrites of their biological
counterparts. A particular type of interconnected neural
net is shown in Fig. 1. In this figure an input layer,
a central or hidden layer, and an output layer are
available. In a network, each connecting line has an
associated weight. Two important abilities of NNs
are the supply of quick solutions to a problem and
the capability of generalizing their answers, providing
acceptable results for unknown samples. In this way,
they learn about the problem under study and the
learning is commonly named training process.
One of the well-known topologies of NN for learning
is the multilayer perception (MLP) which is used for
classification and estimation problems. An example of
layered network is shown in Fig. 1. In this topology
there are L inputs, m hidden units and n output units.
The output of j th hidden unit is obtained by linear
combination of the L inputs as:
(1)
υij aj
where υij is weight going from input i to hidden unit
j . Using an activation function f , the output of neuron
j is obtained as:
L
(2)
υij aj
bj = f
i =0
in which f is activation function. Sigmoid activation
functions are of common interest. Sigmoid tangential
and other functions could be applied in ANN modeling.
ANN training is an optimization process in which
an error function is minimized by adjusting the ANN
weights. When an input training pattern is introduced to
ANN, output is calculated. Output is compared with the
real output provided by the user. This difference is used
by the optimization technique to train the network. The
error function to be minimized in this study is mean
square error (MSE) Ej and is given by Eqn (3):
n
1
Ej =
(Ci − Cir )2
n i =1
where Cir is the i th real target and Ci is the network
output corresponding to the j th input. Thus, training
process is a path from input layer to output layer to
calculate an output, obtaining the error and a backward
path to update the weights. The procedure goes on till
Ej is minimized. During the training process, the train
set error decreases since the ANN weights are adjusted
according to the predicted errors from this set. Training
process should stop when the testing error reaches its
lowest point along the training process.
Besides MLP, another class of networks has been
known in recent years and is called the radial basis
function (RBF) network. The RBF ANN is an alternative network architecture to the MLP. The RBF network
can be regarded as a three-layer structure (Fig. 2) where
the input layer is fully connected by fixed unit weights
to the hidden layer. Each hidden layer node has an associated vector called a center. The node calculates the
Euclidean distance between the training validation center vector and the network input vector and passes the
result through a nonlinear activation function. The output layer does not have activation functions, but simply
forms a linear weighted sum of the hidden layer node
outputs.
The output of the j th hidden node is:
hj = f (x − cj , rj )
V11
ai
I1
Vi1
Ii
W1n
Vij
Wj1
bj WjK
Vim
VL1
aL
IL
CK
Wjn
VLj
Wm1
bm
VLm
Input
Layer
C1
W1K
V1j
V1m
ai
W11
b1
Cn
Hidden
Layer
Output
Layer
Figure 1. Structure of an artificial neural network.
 2008 Curtin University of Technology and John Wiley & Sons, Ltd.
(4)
where x = [x1 . . . xi . . . xni ] is the network input
vector, cj is the center vector of the j th hidden layer
node whose dimension is equal to the dimension, ni , of
x, f is a nonlinear function and ρj is a constant scalar
argument, called the width, of f in the j th hidden layer
node. The output of the network, k th output layer node,
is found from:
WmK
Wmn
(3)
ŷk (x ) =
nc
wjk hj
(5)
j =1
where wjk is the weight connecting the j th hidden layer
node to the k th network output. An RBF network carries
Asia-Pac. J. Chem. Eng. 2008; 3: 357–363
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering
ANN MODELING OF O2 SEPARATION
output must be bounded for any network input and,
consequently, an RBF ANN dynamic model with either
of these bounded basis functions must be stable.
The output of an RBF ANN node is a linear function of the node’s weight parameters and, hence, these
parameters can be determined using a least squares
technique. The well-known recursive least squares algorithm in general form is:
ε(t) = y(t) − ŷ(t) = y(t) − θ̂ T (t − 1)(t)
(11)
θ̂ (t) = θ̂ (t − 1) + L(t)ε(t)
(12)
P (t − 1)(t)
L(t) =
(13)
λ + T (t)P (t − 1)(t)
P (t − 1)(t) T (t)P (t − 1)
1
P (t − 1) −
P (t) =
λ
λ + T (t)P (t − 1)(t)
(14)
Figure 2. The RBF neural network.
where
out a superposition of basis functions and is capable
of universal approximation. The first condition is the
RBF has sufficient hidden nodes as is to be a universal
approximator. The other conditions relate to the type of
basis function and the positioning of centers. A variety
of functions has been proposed including the thin-plate
spline function:
f (z , l ) = z 2 ln(z ),
(6)
the multiquadric function:
f (z , ρ) = (z 2 + ρ 2 )1/2 ,
(7)
the inverse multiquadric function:
f (z , ρ) = (z 2 + ρ 2 )−1/2 ,
(8)
and the Gaussian function:
f (z , ρ) = exp
−z 2
(9)
ρ2
ni
(x (i ) − cj (i ))2
z = x − ci =
For the case of estimating a weight vector for the
k th output node of an RBF ANN, the parameter vector
contains the weight parameters and the regression vector
is formed from the outputs of the hidden nodes, θ (t) =
[w1k . . . wjk . . . wnck], (t) = [h1 . . . hj . . . hnc],
where hj is defined in Eqn (4).
The preceding pages describe RBF modeling of the
hollow fiber membrane.
REQUIRED DATA
where
ε(t) = prediction error
θ̂(t) = parameter estimate vector of θ at time t
L(t) = gain vector
y(t) = target output
(t) = regression or information vector
P (t) = covariance matrix
λ = forgetting factor
1/2
(10)
i =1
Both the Gaussian and the inverse multiquadric
are bounded functions, since they tend to zero as z
tends to infinity. This contrasts with the unbounded or
global nature of the multiquadric and thin-plate spline
functions that tend to infinity as z tends to infinity.
Hence, for an RBF ANN, the Gaussian or inverse
multiquadric function has the advantage over the thinplate spline or multiquadric function that the network
 2008 Curtin University of Technology and John Wiley & Sons, Ltd.
The simulations of processes with NN require a large
number of experimental data. The limitation of application of NNs in simulation of membrane systems is
due to the lack of open experimental information in
industrial membrane gas separation units.
In our study, the software developed by Research
Institute of Petroleum Industry (RIPI) was selected
as a source for producing experimental information.
The RIPI multicomponent model is capable of solving
differential equations related to fiber membrane modules. It is possible to obtain data for multicomponent
mixtures with different values of permeability coefficient and high stage cuts (higher than 95%) by this
model. The model has been developed for three patterns of counter-current, co-current, and diagonal flow.
The model is able to predict the performance of the
Asia-Pac. J. Chem. Eng. 2008; 3: 357–363
DOI: 10.1002/apj
359
360
S. S. MADAENI, G. ZAHEDI AND M. AMINNEJAD
module in the presence or absence of evacuating gas
flow for permeate components. There is a good agreement between the generated data by the RIPI software
and experimental information available in literature.[8]
MODEL ASSUMPTIONS
Principles and assumptions governing the RIPI model
are as follows:
1. Pressure drop along the fibers and shell is negligible.
2. Hollow fiber membrane consists of a thin active
layer that is responsible for separation. This layer
is located on top of a porous support layer. Mass
transfer resistance is related to the active layer.
3. No axial dispersion exists in the direction of gas flow
within the fiber or shell.
4. The gas within the fibers and shell has a plug flow.
5. Performance of one fiber is calculated and the result
is extended to a bundle of fibers within the module to
consider the total gas flow and the entire membrane
surface.
6. The deformation of fibers by pressure is negligible.
7. The Joule-Thompson effect and the temperature
change in the module are insignificant.
8. The whole fibers contain uniform internal and external diameters. The thickness of active layer is constant for all fibers.
9. Membrane module is modeled in steady state conditions.
MODELING
The general method of modeling is that the module is
divided into N sections in the axial direction (Fig. 3).
Mass balance equations are solved for each section. This
model is set to employ the first order finite difference
method rather than a series of difference equations from
partial mass balances that have been expanded for this
problem.[9] In this study the effects of pressure drop are
not considered.
Asia-Pacific Journal of Chemical Engineering
For modeling of a system by neural systems (in this
project RBF model was employed), an input vector and
a target vector can exist in multidimensional space of
an m × n matrix. Input matrix consists of independent
variables that change the system characteristics. For
example, if we assume that in a simple kinetic model,
the output concentration from the reactor depends on
input temperature parameters, input pressure, and initial material concentrations; the input matrix will be a
column vector such that its members are input temperature, input pressure, and initial material concentrations.
Similarly, the output vector can be defined as a matrix
whose members characterize the concentrations of output materials from the reactor.[10]
For membrane separating system, the performance
of module depends on conditions such as feed rate,
constituents and pressure, membrane surface, and permeability. The input vector is defined on the basis of
these parameters. An empirical point is defined for modeling the network. This is a column vector containing
members similar to the defined parameters.
The selected system for this research was a hollow
fiber module for separation of oxygen from air to
produce pure nitrogen. The target vector for this model
is a column vector containing three members that are:
permeation rate, the amount of N2 in the remaining
flow, and the amount of O2 in the permeate flow.
EXPERIMENTAL RIG
The data available in the literature were employed for
verification of the RIPI model. The data were obtained
from a system for separation of oxygen from air.[8]
The system consisted of two parallel modules with
180 polysulfone hollow fibers and effective membrane
area of 389 cm2 for each module. The experiments
were conducted at a temperature of 23 ◦ C and a feed
pressure of 11 bars. The feed rate was changed from
0.5 to 4 Nm3 /h. Different stage cuts were studied to
calculate the molar value of oxygen in permeate flow
and nonpermeable nitrogen in the retentate flow.[8]
Comparison of the obtained experimental data[8] with
the results of the RIPI model for similar conditions
Figure 3. The approach for dividing module for counter-current flow.
 2008 Curtin University of Technology and John Wiley & Sons, Ltd.
Asia-Pac. J. Chem. Eng. 2008; 3: 357–363
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering
ANN MODELING OF O2 SEPARATION
Table 1. Comparison between RIPI simulation data and experimental results (%).
Stage
cut
0.1
0.2
0.4
0.6
0.8
0.9
N2 in retentate
(simulation)
N2 in retentate
(experimental)
O2 in permeate
(simulation)
O2 in permeate
(experimental)
81.51
83.95
87.90
91.40
94.00
95.50
83.5
85.0
89.5
96.0
98.5
99.3
57.5
55.3
51.2
47.0
43.0
41.5
56.0
53.0
49.0
42.5
37.0
35.0
(Table 1) indicates that the RIPI model performance is
acceptable to a large extent.
RESULTS AND DISCUSSIONS
The developed ANN model was employed for studying
variables affecting the separation. One of the variables
was changed in a defined interval and other variables
were kept constant. By this way we obtained several
series of output information for each modeling. This
was the procedure for studying the effect of operational
parameters on the system. A sample of obtained information is illustrated in the following figures.
One of the effective parameters is the permeability
coefficient of the constituents. In the experimental system, permeability of each constituent was measured in
a pure form. However, in practice, a mixture of constituents is available in the feed. The mixture of species
influences the permeability of each component compared to the pure state. Therefore, the calculated values
for permeability do not match the reality, providing
error in the obtained results. A sample of data generated
with RIPI simulation software is presented in Table 2.
In order to evaluate the accuracy of the created model
by NNs for a specified system from the available experimental information in a specified interval, we arbitrarily
selected some of the data during the instruction of network. Two third of the data were employed for training
ANNs. After the creation of network structure from the
experimental data, the software outputs were compared
with the rest i.e. one third of experimental results.
The data created using NN were compared with the
experimental results for various conditions. The graphs
are presented for permeate flow vs feed flow rate
(Fig. 4), molar value of nitrogen in retentate (Fig. 5)
and oxygen in permeate (Fig. 6) vs feed flow rate, mole
fraction of nitrogen in retentate (Fig. 7) and oxygen in
permeate (Fig. 8) vs feed pressure and permeate flow vs
feed pressure (Fig. 9). The indicated graphs demonstrate
the high performance of the created network. All graphs
indicate an appropriate agreement between simulations
of hollow fiber membrane module using NNs with
experimental data.
The simulation is useful for many situations including
unavailability of information for the membrane system, such as, membrane structure and material, membrane thickness, various layers of composite membranes, the diffusivity and permeability coefficients
etc. The NN simulation is based on the experimental results. There is no need for detailed information
of membrane structure and module. This is a highly
positive point for simulation of membrane processes
by NNs.
Table 2. A sample of data generated with the RIPI simulation software.
Run
1
2
3
4
5
6
7
8
9
10
11
12
Feed
flow
(kmol/s)
1.24E
2.24E
3.24E
4.24E
5.24E
6.24E
7.24E
8.24E
9.24E
1.02E
1.12E
1.22E
–
–
–
–
–
–
–
–
–
–
–
–
Feed
pre. (bar)
Memb.
area
(m2 )
06
11
7.576
06 1.10E+01 7.58E+00
06
11
7.576
06
11
7.576
06
11
7.576
06
11
7.576
06
11
7.576
06
11
7.576
06
11
7.576
05
11
7.576
05
11
7.576
05
11
7.576
O2 -per.
N2 -per.
3
2
3
(m /m .s.bar) Selectivity (m /m2 .s.bar)
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
–
–
–
–
–
–
–
–
–
–
–
–
06
06
06
06
06
06
06
06
06
06
06
06
7.33
7.33E+00
7.33
7.33
7.33
7.33
7.33
7.33
7.33
7.33
7.33
7.33
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
–
–
–
–
–
–
–
–
–
–
–
–
07
07
07
07
07
07
07
07
07
07
07
07
Permeate
flow
(kmol/s)
0
2.00E –
2.18E –
2.32E –
2.44E –
2.54E –
2.62E –
2.68E –
2.74E –
2.78E –
2.82E –
2.85E –
06
06
06
06
06
06
06
06
06
06
06
N2 (mole
fraction) in
retentate
O2 (mole
fraction) in
permeate
0.79
1.00E+00
0.99132
0.97469
0.95704
0.94093
0.9269
0.91485
0.90453
0.89564
0.88794
0.88123
0.00E+00
2.35E+01
3.08E – 01
3.62E – 01
4.01E – 01
4.30E – 01
4.52E – 01
4.69E – 01
4.82E – 01
4.93E – 01
5.02E – 01
5.10E – 01
(continued overleaf )
 2008 Curtin University of Technology and John Wiley & Sons, Ltd.
Asia-Pac. J. Chem. Eng. 2008; 3: 357–363
DOI: 10.1002/apj
361
S. S. MADAENI, G. ZAHEDI AND M. AMINNEJAD
Asia-Pacific Journal of Chemical Engineering
Table 2. (Continued).
Feed
flow
(kmol/s)
Feed
pre. (bar)
100
0.00010024
101
4.96E – 05
102
4.96E – 05
103 0.000049 – 611
104
4.96E – 05
105
4.96E – 05
106
4.96E – 05
107
4.96E – 05
108
4.96E – 05
109
4.96E – 05
110
4.96E – 05
111
4.96E – 05
112
4.96E – 05
113
4.96E – 05
114
4.96E – 05
115
4.96E – 05
116
4.96E – 05
117
4.96E – 05
201
4.96E – 05
202
4.96E – 05
203
4.96E – 05
204
4.96E – 05
205
4.96E – 05
206
4.96E – 05
207
4.96E – 05
208
4.96E – 05
209
4.96E – 05
210
4.96E – 05
211
4.96E – 05
212
4.96E – 05
213
4.96E – 05
214
4.96E – 05
215
4.96E – 05
216
4.96E – 05
217
4.96E – 05
218
4.96E – 05
219
4.96E – 05
220
4.96E – 05
11
2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3
3.1
3.2
3.3
3.4
3.5
3.6
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
Memb.
O2 -per.
N2 -per.
area
(m2 ) (m3 /m2 .s.bar) Selectivity (m3 /m2 .s.bar)
7.576
7.576
7.576
7.576
7.576
7.576
7.576
7.576
7.576
7.576
7.576
7.576
7.576
7.576
7.576
7.576
7.576
7.576
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
3.52E
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
06
06
06
06
06
06
06
06
06
06
06
06
06
06
06
06
06
06
06
06
06
06
06
06
06
06
06
06
06
06
06
06
06
06
06
06
06
06
7.33
7.33
7.33
7.33
7.33
7.33
7.33
7.33
7.33
7.33
7.33
7.33
7.33
7.33
7.33
7.33
7.33
7.33
7.33
7.33
7.33
7.33
7.33
7.33
7.33
7.33
7.33
7.33
7.33
7.33
7.33
7.33
7.33
7.33
7.33
7.33
7.33
7.33
Permeate flow against flow rate
3.30E-06
3.20E-06
3.10E-06
3.00E-06
2.90E-06
2.80E-06
2.70E-06
2.60E-06
Predict
Actual
2.50E-06
1
2
6
5
4
7
3
Feed flow rate (kmole/sec)
8
9
Figure 4. Comparison of experimental data with predicted
permeate flow vs feed flow. This figure is available in colour
online at www.apjChemEng.com.
 2008 Curtin University of Technology and John Wiley & Sons, Ltd.
N2 mole fraction in retentate
Run
Permeeate flow (kmole/esc)
362
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
4.80E
9.20E-01
9.00E-01
8.80E-01
8.60E-01
8.40E-01
8.20E-01
8.00E-01
7.80E-01
7.60E-01
7.40E-01
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
Permeate
flow
(kmol/s)
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
3.23E
2.03E
2.28E
2.54E
2.81E
3.08E
3.35E
3.63E
3.92E
4.20E
4.49E
4.79E
5.09E
5.39E
5.69E
6.00E
6.31E
6.62E
4.32E
4.75E
5.18E
5.61E
6.04E
6.47E
6.88E
7.31E
7.74E
8.17E
8.59E
9.02E
9.45E
9.87E
1.03E
1.07E
1.11E
1.16E
1.20E
1.24E
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
06
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
07
06
06
06
06
06
06
O2 (mole
N2 (mole
fraction) in fraction) in
retentate
permeate
0.80253
0.79049
0.7906
0.79073
0.79086
0.791
0.79115
0.79131
0.79147
0.79165
0.79183
0.79202
0.79221
0.79241
0.79262
0.79284
0.79305
0.79328
0.79337
0.79371
0.79404
0.79438
0.79471
0.79505
0.79537
0.7957
0.79604
0.79638
0.79671
0.79705
0.79738
0.79771
0.79805
0.79838
0.79871
0.79905
0.79938
0.79971
5.86E – 01
0.33004
0.34069
0.35086
0.36056
0.36981
0.37864
0.38706
0.39508
0.40273
0.41003
0.41698
0.42361
0.42994
0.43597
0.44173
0.44722
0.45247
0.59345
0.59318
0.59291
0.59263
0.59236
0.59208
0.59182
0.59155
0.59127
0.591
0.59072
0.59045
0.59017
0.58989
0.58962
0.58934
0.58907
0.58879
0.58852
0.58824
N2 mole fraction in retentate ageinst feed flow rate
Actual
1
2
3
4
5
6
7
feed flow rate (kmole/sec)
Predict
8
9
Figure 5. Comparison of experimental data with predicted
N2 in retentate vs feed flow. This figure is available in colour
online at www.apjChemEng.com.
Asia-Pac. J. Chem. Eng. 2008; 3: 357–363
DOI: 10.1002/apj
6.00E-01
ANN MODELING OF O2 SEPARATION
O2 mole fraction in permeate against feed rate
5.80E-01
5.60E-01
5.40E-01
5.20E-01
5.00E-01
4.80E-01
4.60E-01
Predict
Actual
4.40E-01
1
2
3
6
4
5
7
feed flow rate (kmole/s)
8
9
O2 mole fraction permeate
O2 mole fraction in permeate
Asia-Pacific Journal of Chemical Engineering
O2 mole fraction in permeate against feed pressure
3.00E-06
2.50E-06
2.00E-06
1.50E-06
1.00E-06
Actual
5.00E-07
Predict
0.00E+00
1
2
3
4
5
6
7
Feed pressure (barg)
Figure 6. Comparison of experimental data with predicted
8.15E-01
Figure 8. Comparison of experimental data with predicted
O2 in permeate vs feed pressure. This figure is available in
colour online at www.apjChemEng.com.
Permeate flow aganst feed pressure
N2 mole fraction in retante agenst feed pressure
8.10E-01
8.05E-01
8.00E-01
7.95E-01
7.90E-01
Actual
7.85E-01
6.00E-01
permeate flow (kmole/s)
N2 mole fraction in retentate
O2 in permeate vs feed flow. This figure is available in colour
online at www.apjChemEng.com.
Predict
5.00E-01
4.00E-01
3.00E-01
2.00E-01
Actual
1.00E-01
Predict
0.00E+00
7.80E-01
1
2
3
4
5
6
7
8
Feed pressure (bareg)
Figure 7. Comparison of experimental data with predicted
N2 in retentate vs feed pressure. This figure is available in
colour online at www.apjChemEng.com.
1
2
3
6
4
5
Feed pressure (barg)
7
8
Figure 9. Comparison of experimental data with predicted
permeate flow vs feed pressure. This figure is available in
colour online at www.apjChemEng.com.
REFERENCES
CONCLUSIONS
Application of ANNs model can render some difficulties like type of membrane, uncertainty in porosity
and mechanism of adsorption, etc. in simulation of a
membrane module. Based on different training algorithms, RBF has been found as the best network with
minimum training error for modeling of hollow fiber
membrane modules. The obtained results incorporate
excellent capability of ANN in modeling of membrane
processes. The model was successfully used to optimize O2 separation from air in a hollow fiber membrane
module.
 2008 Curtin University of Technology and John Wiley & Sons, Ltd.
[1] R.W. Baker. Membr. Technol., 1999; 138(6), 5–11.
[2] A.S. Kovvali, S. Vemury, K.R. Krovvidi, A.A. Khan.
J. Membr. Sci., 1992; 73(1), 1–23.
[3] R. Qi, M.A. Henson. J. Membr. Sci., 1996; 121, 11–24.
[4] J. Hao, P.A. Rice, S.A. Stern. J. Membr. Sci., 2002; 209,
177–206.
[5] L. Wang, C. Shao, H. Wang, H. Wu. J. Nat. Gas Chem., 2006;
15, 230–234.
[6] E.J. Mogla. Chem. Eng. Process., 2003; 42, 675–695.
[7] A. Laurentiu, B. Tarca, P.A. Grandjean, L. Faı̈çal. Chem. Eng.
Process., 2003; 42(8–9), 653–662.
[8] C. Fabiani, L. Bimbi, M. Pizzichini, L. Santarossa. J. Gas Sep.
Purif., 1996; 10(1), 75–79.
[9] D.T. Coker, B.D. Freeman, G.K. Fleming. AICHE J., 1998;
44(6), 1289–1302.
[10] D.M. Himmelblau, J.C. Hoskins. Comput. Chem. Eng., 1998;
12(9–10), 881–898.
Asia-Pac. J. Chem. Eng. 2008; 3: 357–363
DOI: 10.1002/apj
363
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