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

код для вставкиСкачатьASIA-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. 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