Prediction of ternary gas permeation through synthesized PDMS membranes by using Principal Component Analysis (PCA) and fuzzy logic (FL)

Journal of Membrane Science 360 (2010) 509–521

Contents lists available at ScienceDirect

Journal of Membrane Science journal homepage: www.elsevier.com/locate/memsci

Prediction of ternary gas permeation through synthesized PDMS membranes by using Principal Component Analysis (PCA) and fuzzy logic (FL) Ali Ghadimi, Mohtada Sadrzadeh, Toraj Mohammadi ∗ Research Centre for Membrane Separation Processes, Faculty of Chemical Engineering Iran University of Science and Technology (IUST), Narmak, Tehran, Iran

a r t i c l e

i n f o

Article history: Received 7 February 2010 Received in revised form 18 May 2010 Accepted 25 May 2010 Available online 31 May 2010 Keywords: PDMS membrane Gas separation Permeability Principal Component Analysis (PCA) Fuzzy logic (FL)

a b s t r a c t Implementation of try and error method for membrane preparation procedures is a time and cost consuming technique. This study tries to present a novel idea to make membrane preparation procedure heuristic. Applying this method, helps researchers to predict performance of a membrane prior to its preparation. At first, a number of membranes are prepared and characterized. Then, their measured separation properties are used for prediction of performance of a membrane before its preparation. Furthermore, after preparation of each new membrane, its relevant data can be added to the data bank of the model to improve its capability for the next predictions. Therefore, this model will be improved step by step, after each new preparation. Fuzzy logic-based (FL) model and Principal Component Analysis (PCA) were employed to predict permeability of C3 H8 , CH4 and H2 in ternary gas mixtures using a membrane gas separation module. Based on Placket–Burman (P–B) design, eight different polydimethylsiloxane (PDMS) membranes were synthesized using different preparation conditions, solvent concentration, crosslinker concentration, catalyst concentration, type (or boiling point) of solvent, stirring time and synthesis times in ambient temperature and in an oven at 80 ◦ C, and their gas permeation properties were investigated. In an innovating procedure, effects of operating conditions, including feed temperature, pressure, flow rate, C3 H8 and H2 concentration, as well as preparation conditions on the permeability of gasses through the synthesized membranes were investigated. Basically, in order to develop a FL model to predict permeability of gasses through all the synthesized membranes, synthesis and operating conditions should be considered, simultaneously, and this extends dimensionality of the problem. In all engineering problems, as the number of variables increases, the corresponding data matrix extends. To overcome the problem, PCA method was randomly used for seven of the prepared membranes from P–B design, and it was shown that the first four principal components could describe almost all of the variation in the data matrix. This means that the dimensionality of the problem reduced from 12 to 4. Using the first four principal components, a Sugeno type FL inference system was trained and applied to predict permeability of gasses. FL modeling results showed that there is an excellent agreement between the experimental data and the predicted values, with mean squared relative error (MSRE) of less than 0.0095. The developed model was used for the 8th membrane and its ability to predict separation parameters of this membrane was confirmed. © 2010 Elsevier B.V. All rights reserved.

1. Introduction Recovery of heavier hydrocarbons such as LPG, LNG and volatile organic compounds (VOCs) from gas streams is of great importance economically. When the rates of these gas streams are modest and heavier hydrocarbons are the minor components of these gas streams, employing membrane gas separation process with rubbery membranes such as polydimethylsiloxane (PDMS) becomes rational.

∗ Corresponding author. Tel.: +98 21 77240496; fax: +98 21 77240495. E-mail address: [email protected] (T. Mohammadi). 0376-7388/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.memsci.2010.05.055

PDMS is the most commonly used rubbery membrane material for separation of heavier hydrocarbons from permanent gasses. Recently, many studies have been carried out on transport properties of pure and binary gas mixtures of O2 , N2 , H2 , CO, CO2 , CH4 and C2 –C4 olefins and paraffins using PDMS membrane [1–15]. Most references report pure gas sorption and transport properties [1–7]. However, some mixture permeation properties, which are important for estimating membrane separation performance, have also been reported [8–15]. In order to improve the performance of membrane gas separation process, optimization (operating and design) and analysis of the process should be accomplished. Modeling and simulation are tools to achieve these objectives. However, modeling of a process covers a broad spectrum. At one extreme, there are theoretical

510

A. Ghadimi et al. / Journal of Membrane Science 360 (2010) 509–521

(or parametrical) models based on fundamental knowledge of the process. These models are also called knowledge-based models. At the other end, there are empirical (or non-parametrical) models which do not rely on the fundamental principles which governing the process [16,17]. In gas separation processes, many theoretical models are used in different fields and some of them are applicable for predicting sorption parameters, diffusion parameters and permeability of gasses. These types of models can be very useful for scale-up applications as well as. However, these types of models are mathematically complex, computationally expensive and they ideally require a very detailed knowledge of the gas separation process as well as characterization of the membranes. Therefore, there is a need to find an alternative means for predicting processes performance by exploiting available process data and extending them to unavailable data. Fuzzy logic (FL) inference systems and artificial neural networks are capable of modeling highly complex and nonlinear processes such as gas separation. The main limitation of these types of modeling is that, they only can be utilized for a specific experiment. In spite of their outstanding ability in predicting objective parameters, they are not as flexible as theoretical models to be employed for different membranes. Artificial neural network has been used in a wide range of membrane process applications (reverse osmosis, nanofiltration, ultrafiltration, microfiltration, membrane filtration, gas separation, membrane bioreactor and fuel cell) [18]. In spite of this fact that FL has a strong ability to predict complex processes, there are few records in literature which it has been used for prediction of membrane processes [19–22]. Fuzzy control system was limitedly applied in membrane processes [23–27]. In this study, a FL inference system and PCA were applied to model gas separation process through different PDMS membranes. FL was employed to predict permeabilities of C3 H8 , CH4 and H2 in experimented levels of operating parameters using a laboratory scale gas separation cell. The main feature of this work was to consider membrane synthesis parameters, by introducing a preparation parameter criterion for each one of the synthesized membranes. By this method, a FL-based model was found to acceptably predict permeability of components in a mixed-gas stream even for different membranes, whereas previous works using fuzzy logic and/or neural networks have tried to predict operating parameters just for a certain membrane. It means previous models do not have any flexibility to synthesis parameters and with changing synthesis conditions and preparing a new membrane a new model should be developed [18–22]. As a matter of fact, this study presents a precious tool for estimating separation properties of a membrane before preparation. However, it must be pointed out that prior to this stage, FL model should have a primary data bank regarding different membranes based on preparation parameters. In summary, this study tries to present a method to investigate operating and synthesis parameters simultaneously, by using a unique FL model.

2. Genetic algorithm theory Genetic algorithms are search methods that can be used to solve optimization problems by implementing powerful search techniques to find an optimal solution within a large search space (possible solutions to the problem). Genetic algorithm techniques are based on natural biological evolution [28]. A genetic algorithm works by generating a large set of possible solutions to a given problem. It then evaluates each of these solutions, and decides on a “fitness level” which is closer to the optimal solution. These solutions then breed new solutions. The parent solutions that were more fit are more likely to reproduce, while those that were less fit are less likely to do so. GA operators, mainly crossover and

mutation, achieve the reproduction of solutions [29]. Crossover combines the features of two parent chromosomes (solutions) to form two new similar children (new solutions) by swapping corresponding segments of parents [30]. Mutation is done by randomly changing one or more genes (parameters within a solution), by a random change with a probability equals to mutation rate. Crossover is aimed at exchanging information between different potential solutions, while mutation is aimed at introducing some extra variability into the population [31]. 3. PCA theory PCA is one of the multivariate methods of analysis and has been used widely with large multidimensional data sets. The use of PCA allows the number of variables in a multivariate data set to be reduced, while retaining as much as possible of the variation present in the data set. This reduction is achieved by taking p variables X1 , X2 , . . ., Xp and finding the combinations of these to produce principal components (PCs) PC1 , PC2 , . . ., PCp , which are uncorrelated. These PCs are also termed eigenvectors. The lack of correlation is a useful property as it means that the PCs are measuring different “dimensions” in the data set. Nevertheless, PCs are ordered so that PC1 exhibits the greatest amount of the variation, PC2 exhibits the second greatest amount of the variation, PC3 exhibits the third greatest amount of the variation, and so on. That is var (PC1 ) ≥ var (PC2 ) ≥ var (PC3 ) ≥ . . . ≥ var (PCp ), where var (PCi ) expresses the variance of PCi in the data set being considered. Var (PCi ) is also called the eigenvalue of PCi . When using PCA, it is hoped that the eigenvalues of most of the PCs will be so low as to be virtually negligible. Where this is the case, the variation in the data set can be adequately described by means of a few PCs where the eigenvalues are not negligible. Accordingly, some degree of economy is accomplished as the variation in the original number of variables (X variables) can be described using a smaller number of the new variables (PCs). Principal Component Analysis can be described as a transform of a given set of n input vectors (variables) with the same length K formed in the n-dimensional vector x = [x1 , x2 , . . ., xn ]T into a vector y according to y = A(x − mX )

(1)

This point of view enables to form a simple Eq. (1) but it is necessary to keep in the mind that each row of the vector x consists of K values belonging to one input. The vector mX in Eq. (1) is the vector of mean values of all input variables defined by the following relation: 1 XK K K

mX = E{X} =

(2)

k=1

Matrix A in Eq. (1) is determined by the covariance matrix CX . Rows in the A matrix are formed from the eigenvectors of CX ordered according to corresponding eigenvalues in descending order. The evaluation of the CX matrix can be performed by the following relation: 1 XK XKT − mX mTX K K

CX = E{(X − mX )(X − mX )T } =

(3)

k=1

As the vector x of input variables is n-dimensional, it is obvious that the size of CX is n × n. The elements CX (i, i) lying in its main diagonal are the variances CX (i, i) = E{(Xi − mi )2 }

(4)

A. Ghadimi et al. / Journal of Membrane Science 360 (2010) 509–521

511

Fig. 1. ANFIS architecture of the input–output system.

of x and the other values CX (i, j) determine the covariance between input variables xi , xj . CX (i, j) = E{(Xi − mi )(Xj − mj )}

(5)

The rows of A in Eq. (1) are orthonormal so the inversion of PCA is possible according to the following relation: X = AT y + mX

(6)

4. FL theory FL was initiated in 1965 by Lotfi A. Zadeh, professor for computer science at the University of California in Berkeley. Basically, FL is a multivalued logic that allows intermediate values to be defined between conventional evaluations like true/false, yes/no, high/low, etc. Notions like rather tall or very fast can be formulated mathematically and processed by computers, in order to apply a more human-like way of thinking in the programming of computers [32]. The use of fuzzy set theory allows the user to include the unavoidable imprecision in the data. Fuzzy inference is the actual process of mapping from a given set of input variables to an output based on a set of fuzzy rules. The essence of the modeling is to identify fuzzy rules. Four fundamental units are necessary for the successful application of any fuzzy modeling approach. These are, namely, the fuzzification unit, the knowledge base (which is composed of the database and the rule base), the inference engine unit and the defuzzification unit. In the fuzzification unit, the input and output variables are fuzzified by considering convenient linguistic subsets such as high, medium, low, heavy, light, hot, warm, big, small, etc. Partition of variable into groups is not a very easy task. Various methods have been developed in the literature, such as the neural network-based method [33], the inductive learning [34], the genetic algorithm [35], the fuzzy clustering [36] and the uses of statistics [37]. In knowledge base unit, fuzzy IF–THEN rules are constructed based on the expert knowledge and/or on the basis of available data. The rules provide a transition between input and output fuzzy sets. Premise part input fuzzy membership functions (MFs) are combined interchangeably with a logical “and” or “or” conjunction whereas the rules are combined with the logical “or” conjunction. In the inference engine unit, the implication part of a fuzzy system is defined as the forming of the consequent membership functions based on the membership degrees of the premise (antecedent) part.

In the defuzzification unit, the result appears as a fuzzy set is defuzzified to calculate a crisp value, which is asked for engineering applications. In the applications of the fuzzy system in control and forecasting, there are mainly two approaches, namely, Mamdani and Sugeno methods [38]. For the first approach, there are clear procedures, i.e. fuzzification, inference and defuzzification procedures. The main difference between Mamdani and Sugeno approaches is originated from defuzzification procedure. In the Mamdani approach, each IF–THEN rule produces a fuzzy set for the output variable, and hence the step of defuzzification is indispensable so as to obtain crisp values of the output variable. However, in Sugeno method, outcome of each IF–THEN inference rule is a scalar rather than a fuzzy set for the output variable. Defuzzification procedure is completed simply in Sugeno method by taking the weighted average of the rule outcome. The main problem with the Sugeno FL modeling is related to the choice of the parameters. For this reason, the adaptive networkbased fuzzy inference system (ANFIS) methodology is applied to estimate the parameters of the membership and the consequent functions [39]. The general scheme of the ANFIS is shown in Fig. 1. Fig. 2 depicts the two-dimensional input space where X1 and X2 are partitioned into four symmetric triangular fuzzy sets. The Sugeno approach has fuzzy sets in the premise part only and IF–THEN control rules are given as follows: Rr :

(1)

(2)

(n)

IF X1 is Sr , X2 is Sr , . . . . . . . . . , Xp is Sr THEN Yr = fr (X1 , X2 , . . . . . . . . . , Xn )

(7)

(i)

where Sr is a fuzzy set corresponding to a partitioned domain of the input variable Xi in the rth IF–THEN rule, n is the number of input variables, fr is a function of the n input variables, and finally Yr is the output of the rth IF–THEN inference rule Rr . The general algorithm of the Sugeno inference system is expressed as follows [38]. It is assumed that there are Rr (r = 1, 2, 3, . . ., k) rules in the above mentioned form. 1- For each implication Ri , Yi is calculated by the function fi in the consequence part: Yi = fi (X1 , X2 , . . . , Xn )=cr (0) + cr (1)X1 + cr (2)X2 + · · · + cr (n)Xn (8) 2- The weights are calculated as follows: rr = (mr1 ∧ mr2 ∧ . . . mrn )P r

(9)

512

A. Ghadimi et al. / Journal of Membrane Science 360 (2010) 509–521

used as the carrier gas. In order to detect and separate peaks of H2 , CH4 and C3 H8 , a rampaed heating program was used for GC column. At first, H2 and CH4 were detected at 25 ◦ C. Then, the column temperature was increased up to 90 ◦ C at 7 ◦ C/min. The column temperature maintained at 90 ◦ C for 10 min and finally C3 H8 peak was detected. The applied TCD current was 60 mA. Permeate flow rate was measured using a Bubble Flow Meter (BFM). In most of the experiments, a digital Mass Flow Meter (MFM) was used instead of the BFM for convenience. The MFM was formerly calibrated by the BFM. At steady state condition, gas permeability of species i was calculated using the following equation: Pi =

22, 414 l p1 dV y A (p2 xi − p1 yi ) RT i dt

(11)

where A is the membrane area (cm2 ), p2 and p1 are feed or upstream and permeate or downstream pressures (atm), respectively, R is the universal gas constant [6236.56 cm3 cm Hg/(mol K)], T is the absolute temperature (K), xi and yi are the mole fractions of species i in the feed and the permeate streams, dV/dt is the volumetric displacement rate of the soap film in the BFM (cm3 /s) and 22,414 is the number of cm3 (STP) of penetrants per mole. 5.2. Module Fig. 2. Fuzzy partition in the two-dimensional space.

where mr1 ∧ mr2 ∧ . . . mrn denote the ˛ cuts of membership functions according to input values for the rth rule. An ∝ cut of a fuzzy set A (A∝ ) is a crisp set, which contains all the elements in U that have membership values greater than or equal to ∝ (x ∈ U|membership function ≥ ∝) in A. The universe of discourse U is the n-dimensional Euclidean space Rn . The occurrence probability is shown by Pr and sˆ tands for min or production operation. For the sake of simplicity Pr is taken as equal to 1. 3- The final output Y inferred from k implications is given as the weighted average of all Yr with the weights rr as:

n r Y r=1 r r Y=  n r r=1 r

(10)

5. Materials and method 5.1. Setup Gas permeation experiments are one of the most important methods for finding the structure and morphology of synthesized PDMS membranes. In order to carry out these experiments, a set up was assembled (Fig. 3). H2 and CH4 gasses with purity of 99.5% supplied by Technical Gas Services, Inc. and C3 H8 gas with purity of 99.9% supplied by Air Products and Chemicals, Inc. were used as feed gasses. The feed flow rate was controlled by Brooks Mass Flow Controllers (MFC), model 5850 E (0–18,000 normal mL/min range). Constant transmembrane pressure was controlled by a Back Pressure Regulator (BPR), model 26.60 SCFBXE262C086. As shown in Fig. 3, H2 , CH4 and C3 H8 gasses were mixed with an appropriate ratio in a mixing vessel and the gas mixture was sent to the module. Before that, gas temperature was adjusted using a P&ID temperature control system (TCS). Before reaching to the target temperature, the gas mixture was sent off via a vent line. After acquiring this temperature, the gas was fed to the upstream side with the vent line closed. The gas temperature is controlled to ±1 ◦ C using this TCS. Permeate stream was sent to a gas chromatography instrument (GC-2001M, Sanayeh Teif Gostar Co., Iran) with a thermal conductivity detector (TCD) and a chromosorb-102 column. Argon was

A crossflow membrane cell made from stainless steel (grade 316) was used to conduct the experiments (Fig. 4). The membrane was housed in the cell that consisted of two detachable parts. Rubber O-rings were used to provide a pressure-tight seal between the membrane and the cell. The membrane had an effective area of approximately 10 cm2 . 5.3. Membrane preparation PDMS films were prepared based on P–B experimental design. Casting solutions were initially prepared from toluene solutions containing a specified wt.% Dehesive 944 silicone (Wacker Silicones Corporation, Adrian, MI) with proper amounts of crosslinker (V24, Wacker) and catalyst (OL, Wacker). As supplied by the manufacturer, Dehesive 944 is a solvent-based addition crosslinkable silicone. Films were prepared by pouring the polymer solution into a glassy casting die supported by a Teflon-based polymer. The cast films were dried slowly under ambient conditions. They were then placed in an oven at 80 ◦ C to remove residual solvent and to fully crosslink the polymer. After they were cooled to room temperature, the crosslinked films were easily removed from the Teflon-based polymer. Finally, the thin films were detached from the glassy die using a very sharp razor. The resulting PDMS films were transparent and not tacky. Thickness of the films was determined with a digital micrometer (Mitutoyo Model MDC-25SB) readable to ±1 ␮m and found to be approximately 250 ␮m. The synthesized membranes were housed in the gas permeation module. 5.4. Design of experiment 5.4.1. Design of experiment for membrane preparation To optimize the design of an existing process, it is necessary to identify which factors have the greatest influence and which values produce the most consistent performance. Experimenting with the design variables one at a time or by trial and error until a first feasible design is found, is a common approach to design optimization. However, this approach can lead to a very long and expensive time span for completing the design process. Using factorial design of experiments (DOEs), a technique for laying out experiments when multiple factors are involved, helps researchers to determine the

A. Ghadimi et al. / Journal of Membrane Science 360 (2010) 509–521

513

Fig. 3. Schematic view of the experimental setup.

Fig. 4. Schematic view of the experimental module.

possible combinations of factors and to identify the best combination. However, in industrial settings, it is extremely costly to run a number of experiments to test all combinations. Hence, it is necessary to apply design techniques that economically permit DOEs with many factors. These are the screening designs that can be used for at least four factors to more factors that can be practically handled in an experiment. Their purpose is to identify or screen out those factors that merit further investigation [40–43]. In a fractional factorial experiment, only a fraction of the treatment combinations are observed. This has the advantage of saving time and money in running the experiment, but has the disadvantage that each main effect and interaction contrast will be confounded with one or more other main effect and interaction contrasts and cannot be estimated separately [40–42]. P–B designs are saturated fractional factorial designs which were invented by Placket and Burman in 1946. In the context of fractional factorial experiments, a saturated design is one that uses only n = p + 1 treatment combinations to estimate the main effects of p factors independently (assuming that all interactions are negligible) [42,43]. In this study, an eight run P–B design was used to investigate the effect of seven preparation factors, each at two low (−) and high (+) levels, on the permeability of pure gasses through the synthesized PDMS membranes (Table 1). Then, a standard analytical procedure was followed and preparation factors were ranked based on their

calculated effects [43]. Factors which are assumed to affect permeation properties of synthesized membranes and their relevant levels are as follows: A: Solvent concentration: 50% (2.5 g oil + 2.5 g solvent) and 80% (2.5 g oil + 10 g solvent). B: Crosslinker concentration (14 and 42 ␮L). C: Catalyst concentration (18 and 54 ␮L). D: Type of solvent or boiling point of solvent (toluene, hexane). E: Stirring time (0.5 and 2 h). F: Synthesis time in ambient temperature (1 and 3 days). G: Synthesis time in an oven at 80 ◦ C (2 and 24 h).

Table 1 The applied saturated orthogonal main effect plan for 7 factors and 8 observations. A

B

C

D

E

F

G

+ + + − + − − −

− + + + − + − −

− − + + + − + −

+ − − + + + − −

− + − − + + + −

+ − + − − + + −

+ + − + − − + −

514

A. Ghadimi et al. / Journal of Membrane Science 360 (2010) 509–521

Table 2 Operating conditions and compositions of flue gas stream in Shiraz Oil Refinery (Shiraz, Iran). Compound

H2

CH4

C2 H6

C3 H8

n-C4 H10

i-C4 H10

n-C5 H12

i-C5 H12

C6+

H2 S

Mole percent

61.6

19.5

3.2

11.5

1.4

1.7

0.3

0.5

0.2

5 ppm

Operating data

Flow rate (m3 /h)

Pressure (atm)

Temperature (◦ C)

4200

6.8

38

5.4.2. Design of experiment for mixed-gas permeation For each one of the synthesized membranes a full factorial design of experiments was applied to investigate the effect of pressure, temperature, flow rate, C3 H8 and H2 concentrations on permeability of C3 H8 , CH4 and H2 . Each parameter was examined at three levels and 35 = 243 experiments were conducted: • • • • •

gas mixture) is resulted from the larger negative Hs value. On the other hand, the permanent feed gas components, H2 and CH4 , exhibit slightly positive activation energy of permeation (4.78 and 8.91 kJ/mol), which leads to a decrease in their permeabilities by decreasing the feed temperature. Increasing C3 H8 concentration in the feed leads to an increase in all components permeability (Fig. 5d). The increase in permeability is due to C3 H8 -induced swelling of the PDMS film caused by increased C3 H8 sorption at higher partial pressures in the feed. Swelling of PDMS by hydrocarbon vapors was reported in the literature. For example, De Angelis et al. reported 30 vol% swelling of PDMS upon exposure to C3 H8 at 7 atm [48]. Swelling leads to higher chain mobility of the polymer, which results in a more significant increase in the diffusion coefficient of the smaller permanent gas components (H2 and CH4 ) relative to that of the larger organic vapor (C3 H8 ). Jordan and Koros [49] reported an increase in CH4 permeability with increasing CO2 fugacity CH4 permeability in PDMS increased from 1700 Barrer in pure gas experiments at 35 ◦ C to 2500 Barrer in a 50/50 CO2 /CH4 mixture at a CO2 fugacity of 27 atm and the same temperature. Pinnau and He [50] observed an increase in CH4 permeability in PDMS in the presence of n-C4 H10 . For instance, at 35 ◦ C, CH4 permeability increased from 1300 Barrer (pure gas) to 1450 Barrer when the polymer was exposed to an n-C4 H10 /CH4 mixture having an n-C4 H10 relative pressure (p/psat ) of 0.38. They speculated that this behavior is due to an increase in CH4 diffusion coefficient as a result of the polymer swelling (i.e., plasticization) by n-C4 H10 .

Feed pressure: 5, 6 and 7 atm. Feed temperature: 35, 40 and 45 ◦ C. Feed flow rate: 40, 50 and 60 cm3 /s. C3 H8 concentration in feed: 15, 20, 25%. H2 concentration in feed: 55, 60, 65%.

These parameters and their relevant levels were selected based on condition of flue gas stream in Shiraz Oil Refinery (Shiraz, Iran). Operating conditions and compositions of the flue gas stream are presented in Table 2. According to the data presented in this table, pressure, temperature and feed composition in laboratory scale are in the range of industrial scale. C3 H8 , CH4 and H2 gasses were selected as the representatives of heavier hydrocarbons, lighter hydrocarbons and permanent gasses, respectively. 6. Results and discussion 6.1. Experimental results Fig. 5(a–c) presents the influence of upstream pressure on C3 H8 , H2 and CH4 permeabilities in PDMS in ternary gas mixture containing 15, 55 and 30 vol% of these gasses, respectively, from 35 to 45 ◦ C. As can be seen, permeability values of C3 H8 decreases with increasing feed pressure, whereas those of H2 and CH4 increase. The permeability reduction of C3 H8 may be due to the competitive sorption, which results in almost constant (or slightly increasing) solubility coefficient (the ratio of gas concentration in the polymer to its partial pressure) for each component. At the same time, Synthesis parameters A

B

C

6.2. Data analysis The original data matrix consists of two parts. The first part contains synthesis parameters, and the second one includes operating conditions. Therefore, each row of this data matrix can be depicted as follows:

Operating parameters D

E

F

G

Temperature

the polymer swells and this results in much higher diffusivity for smaller molecules such as H2 and CH4 compared to larger ones such as C3 H8 due to the competitive diffusion. The net result is an increase in the H2 and CH4 permeabilities and a decrease in the C3 H8 permeability [44–47]. The mixed-gas permeation property of the synthesized PDMS film was also determined as a function of temperature with the same gas mixture, as shown in Fig. 5(a–c). As expected, for a rubbery polymer film, the C3 H8 permeability increases by decreasing the feed temperature (Fig. 5a). The increasing C3 H8 permeability is reflected from the negative activation energy of permeation, Ep . The activation energy of permeation is the sum of the activation energy of diffusion, Ed , and the heat of sorption, Hs [9]. Because Ed is always positive in an activated diffusion process, the negative Ep value for C3 H8 (Ep = −18.31 kJ/mol for the 1st membrane in P–B design, at 5 atm feed pressure using 15/55/30 C3 H8 /H2 /CH4 ternary

Pressure

Feed flow rate

C3 H8 concentration

H2 concentration

In the next step, seven synthesized membranes from P–B design were tested by using the laboratory scale set up, and permeability of C3 H8 , CH4 and H2 were measured. Each row of this matrix has valuable information about synthesis and operating conditions. Therefore, the final data matrix has the dimension of, 1701 × 12, which cannot be used as an input data matrix in FL method. Number of the input variables is too much, (a 12 input system), and the simplest FL model for a system with this amount of variables is very complicated and time consuming to solve (each one of the columns of the data matrix represents an independent variable for FL model). Note: The data matrix includes all information about synthesis and operating condition of the seven synthesized membranes. All information for each one of the membranes makes a part of the data matrix, 243 × 12. Moreover, it should be mentioned, since the first seven columns of the data matrix introduce synthesis parameters, for a certain membrane all rows of these seven columns are same.

A. Ghadimi et al. / Journal of Membrane Science 360 (2010) 509–521

515

Fig. 5. Effect of feed pressure and temperature on permeability of (a) C3 H8 , (b) H2 and (c) CH4 using 15/55/30 C3 H8 /H2 /CH4 ternary gas mixture, and (d) effect of C3 H8 concentration in feed on permeability of penetrants at 35 ◦ C feed temperature, 5 atm feed pressure and 55 vol% H2 concentration.

As mentioned above, number of the input variables is too much, so the dimension of this data matrix should be reduced. To do so, the first seven columns of the data matrix which introduce synthesis parameters should be defined mathematically. As mentioned earlier there are two levels for each synthesis parameter (high and low). These two levels are represented with two different numbers, 1 and 2 for low and high levels, respectively. For example, the first seven columns of the data matrix for two membranes, 1st and 2nd from P–B design, can be illustrated as follows:

Membrane 1, K (level of parameters) Membrane 2, K (level of parameters)

A

B

C

D

E

F

G

2 2

1 2

1 1

2 1

1 2

2 1

2 2

Basically, changing the synthesis parameters affects separation properties of the synthesized membranes. Therefore, a preparation parameter criterion for each one of the synthesized membranes must be defined, as a function of the synthesis parameters. In order to determine this preparation parameter criterion, different correlations were considered based on the synthesis parameters. Finally, the best correlation for obtaining the preparation parameter criterion was selected. This correlation is given as follows: ϕ=

7 i=1



ωi2 × i

i =

1 0

if K(level of parameters) = 2 if K(level of parameters) = 1 (12)

where ωi is weight value for each one of the synthesis parameters. It should be mentioned that two membranes with different synthesis condition act differently even with a same operating condition. Therefore, this parameter, Ø, was obtained for each one of the synthesized membranes with attention to the synthesis param-

eters, while the operating parameters do not have any effect on it. Obviously, each one of the synthesis parameters has a different contribution in final properties of a synthesized membrane, and these contribution can be depicted by their weight values. To determine the weight values of the preparation parameters genetic algorithm was applied. As mentioned above, this optimization method works with generating solutions by randomly selecting values for the objective parameters. These weight values are evaluated using the fitness function. The fitness function is based on minimization of mean squared relative error, MSRE, between the experimental data and the predicted values by developed model in this study. The parameters values of genetic algorithms used are given in Table 3. Obtained weight values from GA and effectiveness percentage of the synthesis parameters on separation properties of the synthesized membranes which have been determined by following equation are given in Table 4. Effectiveness precentage =

ωi

7

i=1

(13) ωi

As mentioned, synthesis parameters have different effects on separation properties of the membranes. Thus, for considering

Table 3 Values of genetic algorithm parameters. Parameter

Value

Number of generations Population size Number of parameters Crossover rate Mutation rate

200 100 7 80% 20%

516

A. Ghadimi et al. / Journal of Membrane Science 360 (2010) 509–521

Table 4 Weight values and effectiveness percentage of the synthesis parameters.

Weight value (␻) Effectiveness percentage (%)

A

B

C

D

E

F

G

8.4 ± 0.26 17

15.8 ± 0.45 32

9.8+0.56 20

7.1 ± 0.86 14

4.8 ± 0.64 9

2.7 ± 0.11 5

1.4 ± 0.4 3

Table 5 The first four PCs’ parameters. Principal component number

Eigenvalue of covariance (X)

Percent of variance captured by this PC

Percent of variance captured, total

1 2 3 4

5.025 1.762 1.714 1.319

41.872 14.683 14.284 10.992

41.872 56.554 70.838 81.830

these effects on the data matrix, all rows of the input matrix were multiplied by the preparation parameter criterion of the related membrane. (The original data matrix includes information of seven different membranes, and each row of this matrix is multiplied by its own preparation parameter criterion.) For instance, preparation parameter criteria for the first and the second membranes were calculated as follows: ϕmembrane 1 = 8.42 + 7.12 + 2.72 + 1.42 = 130.22, and ϕmembrane 2 = 8.42 + 15.82 + 4.82 + 1.42 = 345.2. In the next step, the PCA method was used for reducing the data matrix dimension. The main challenge of PCA is to determine the number of relevant PCs. Choosing the correct number of PCs is important since noise can be included by using too many PCs or some useful information can be excluded if too few PCs are taken into account [51]. The percent of total variation that each PC describes can be utilized to determine the number of PCs. In cases where the PCA model is applied to, e.g. process control, more sophisticated methods such as cross-validation or eigenvalues of PCs should be preferred as criterion for model dimensionality. The amount of variation described by each PC is presented in Table 5. It can be seen that nearly all the variation is described by the first four PCs. This means that the samples can be plotted on a plane with four-dimensions. 6.3. FL model A sophisticated intelligent model, based on the Sugeno fuzzy modeling principles, was used to predict the permeability of C3 H8 , H2 and CH4 . Data spaces were partitioned into fuzzy sets by means of the grid partitioning method. Training, validating and testing were accomplished with the aid of MATLAB software (version 7.1). ANFIS methodology with hybrid learning method was applied to estimate the parameters of the applied two-parametric Gaussian membership function and the consequent functions. The symmetric Gaussian function depends on two parameters  and c as given by: A (x) = e

(−(x−c)2 )/2 2

(14)

where c and  are the centre and the width of the fuzzy set A, respectively. 6.3.1. Training, validating and testing the ANFIS The reduced data matrix, made by PCA, was introduced to the ANFIS as the input data matrix. This data matrix includes 1701 rows and 4 columns [1701 × 4] which the columns are the first four PCs, including membrane synthesis and operation conditions information. Also, permeability of each one of the gasses was provided as the output parameter of the ANFIS. With the aid of MATLAB programming software 1001 data was randomly picked up in each run

for training and the rest was divided into two subsets for validating and testing, equally. Training procedure was continued until the mean squared relative error, MSRE, versus epoch, each time presenting whole training data set to the inference system, showed rising trend in 10 sequence epoch for validating and/or testing data sets. By this way the optimum number of epochs for this certain FLbased model was obtained. The ANFIS model structure applied for training and testing of the developed model in this study includes 4 input variables and 2 Gaussian membership functions for each variable. Note: A unique inference system cannot be employed for predicting permeability of the all gasses, so in this model three inference systems were used. The input data matrices of these three inference systems are completely similar, but their outputs which are permeability of the gasses are different. Detailed description of model development procedure is shown in Fig. 6. 6.3.2. FL model performance Different groups of training data were examined and with respect to the mean squared error (MSE) of testing data, the proper model was developed. MSE was calculated as follows:



MSE =

N

(Pcal − Pexp )2

(15)

N

where subscripts cal and exp denote calculated and experimental values of P, respectively. N is the number of training, validating and testing data. The most widely used criteria including MSE, root mean square error (RMSE), correlation coefficient (R), coefficient of determination (R2 ) and MSRE for training and testing data sets are presented in Tables 6 and 7. RMSE is the square root of MSE presented in Eq. Table 6 Statistical criteria for evaluation of permeability (training). Criterion

C3 H8

CH4

MSE RMSE R R2 MSRE

45.373 × 10 655.9 0.9796 0.9597 0.0059

4

H2

0.35744 × 10 58.434 0.9794 0.9592 0.0056

4

5.6316 × 104 230.2 0.9764 0.9533 0.0091

Table 7 Statistical criteria for evaluation of permeability (validating and testing). Criterion

C3 H8

MSE RMSE R R2 MSRE

46.303 × 10 665.6 0.9745 0.9497 0.0052

CH4 4

H2

0.59539 × 10 74.39 0.9482 0.899 0.0095

4

6.0751 × 104 237 0.9752 0.951 0.0082

A. Ghadimi et al. / Journal of Membrane Science 360 (2010) 509–521

517

Fig. 6. The PCA–FL model development procedure.

(15). In probability theory and statistics, R indicates the strength and direction of a linear relationship between two variables. In general statistical usage, R refers to the departure of two variables from independence. A number of different coefficients are used for different situations. The best known is the Pearson product-moment correlation coefficient as follows:

 R=

 N

N

(Pcal − Pcal,ave )(Pexp − Pexp,ave )

(Pcal − Pcal,ave ) ×



N

(Pexp − Pexp,ave )

(16)

R2 can have only positive values ranging from R2 = +1.0 for a perfect correlation (positive or negative) down to R2 = 0.0 for a complete absence of correlation. The advantage of R is that it provides the positive or negative direction of the correlation. The advantage of R2 is that it provides a measure of the strength of the correlation. It can be said that R2 represents the proportion of the data that is the closest to the line of best fit.

Another measure of fit is MSRE which is calculated by the following equation: 1 MSRE = N N



Pcal − Pexp Pexp

2 (17)

In Fig. 7 the experimental results (training, validating and testing data) versus fuzzy model predictions are plotted. According to this figure and data presented in Tables 6 and 7, excellent fitness of fuzzy predicted values with experimental data is realized. 6.3.3. FL predictability and generalization After developing an efficient FL-based model, it can be used for prediction of permeability of C3 H8 , CH4 and H2 , for different inputs in the domain of training data. The experimental results versus fuzzy logic predictions for three subsets of data are plotted in Fig. 7. Fig. 7(a, c, and e) shows performance of FL model at the minimum MSRE of training data for permeabilities of C3 H8 , CH4 and H2 , respectively. According to the prediction results for the validating

518

A. Ghadimi et al. / Journal of Membrane Science 360 (2010) 509–521

Fig. 7. Performance of the FL model in predicting permeability of C3 H8 , CH4 and H2 . (a, c and e): training- (b, d and f): validating and testing of C3 H8 , CH4 and H2 .

and testing data, shown in Fig. 7(b, d, and f), it is found out that performance of FL model is acceptable. For better assessing of FL model prediction, functionality of permeability of C3 H8 and its first derivative (sensitivity analysis), versus operating parameters for the 1st synthesized membrane are presented in Figs. 8 and 9, respectively. As can be seen, increasing feed temperature and feed pressure decrease the permeability of C3 H8 , while increasing C3 H8 concentration in feed and feed flow rate, increase C3 H8 permeability. With paying attention to the results of sensitivity analysis, Fig. 9(a and b), increasing feed temperature and pressure decreases permeability of C3 H8 (according to negative first derivative). Additionally, rate of reduction of C3 H8 permeability increases at higher temperature and pressure. Positive first derivative in Fig. 9(c) shows an increasing trend for permeability of C3 H8 with increasing its concentration in feed. However, there is a specific concentration after which, increasing rate of C3 H8 permeability decreases. Increasing C3 H8 concentration in feed increases membrane swelling capability, which subsequently increases C3 H8 permeability. Similarly after a certain level of C3 H8 concentration in feed, the membrane reaches to its saturated condition, so that propensity to absorb a

higher amount of C3 H8 into membrane matrix decreases, slowly. For investigating effect of feed flow rate on permeability of C3 H8 , it should be pointed out that there are two different factors that have contradictory effects on permeability of C3 H8 . The first factor is collision of C3 H8 molecules with the membrane surface and the second one is resistance time of gasses in the module. Permeation of C3 H8 increases with increasing feed flow rate, which is due to better gas mixing. However, increasing rate of C3 H8 permeability decreases due to resistance time reduction. Hence, after a certain feed flow rate, permeability of C3 H8 decreases with increasing flow rate Fig. 9(d). In order to rationalize all this behavior mentioned above, gas transport mechanism in dense polymeric membranes should be discussed. Gas transport through a non-porous polymeric membrane is known to follow the solution-diffusion mechanism (P = DS). According to this three-step mechanism, the gas first sorbs into the membrane at the high-pressure side, then diffuses across the membrane under a partial pressure driving force and finally desorbs from the membrane at the low pressure side. Therefore, gas permeability through the membrane is dependent both on solubility of the gas in the polymer as well as its diffusion in the polymer. Gas

A. Ghadimi et al. / Journal of Membrane Science 360 (2010) 509–521

519

Fig. 8. Comparison FL prediction with experimental data effect of (a) temperature, (b) pressure, (c) concentration of C3 H8 and (d) feed flow rate at medium levels of other factors.

Fig. 9. Sensitivity analysis by the FL model; effect of (a) temperature, (b) pressure, (c) concentration of C3 H8 and (d) the feed flow rate.

520

A. Ghadimi et al. / Journal of Membrane Science 360 (2010) 509–521

boundary layer on sorption of C3 H8 molecules diminishes, and consequently, their solubility and permeation increase. As can be observed, not only does the introduced FL model have an acceptable ability to predict the amount of permeability of different gasses, but also it can give correct prediction for functionality of this objective parameter (permeability of the gasses) with operating parameters. In the last step of this study, FL model was tested for the 8th synthesized membrane. It should be mentioned that FL model data bank did not have any information regarding this membrane. Performance of FL model at the minimum MSRE of testing data for the 8th membrane is shown in Fig. 10. As can be observed, the developed model can predict permeability of gasses through this membrane outstandingly. It can be observed that the model is able to predict a PDMS membrane performance before synthesis. Fig. 10. Performance of FL model in predicting permeability of C3 H8 , CH4 and H2 .

7. Conclusion solubility in polymers typically increases with increasing gas condensability, in the absence of specific interactions between the gas molecules and the polymer chains. On the other hand, gas diffusion coefficients decrease with increasing penetrant size. This is due to this fact that larger molecules interact with more segments of the polymer chains and this favors the passage of smaller molecules such as H2 over larger ones such as C3 H8 . Thus, differences in molecular size and/or gas condensability can result in different gas permeation rates through a polymer. Differential permeation rates result in increasing concentration of the faster permeating species in downstream side of the membrane as compared with their concentrations in the feed stream, thus performing an effective separation of the gasses in the mixture. This phenomenon is the underlying principle of membrane-based gas separation. Hence, in glassy, rigid polymers, such as polysulphone (PS), permeant diffusion coefficient is more important than its solubility coefficient. Therefore, these polymers preferentially permeate the smaller, less condensable gasses, H2 and CH4 over the larger, more condensable gasses, C3 H8 . On the other hand, in rubbery polymers such as PDMS, permeant solubility coefficient is more important. Thus, these polymers preferentially permeate the larger, more condensable gasses over the smaller, less condensable gasses. When feed temperature increases condensability of higher gasses such as C3 H8 decreases significantly while mobility or diffusivity of these gasses increase slightly. On the other hand, diffusivity of smaller molecules such as H2 and CH4 increases considerably with increasing temperature. Thus, increasing temperature has an inverse effect on permeability of C3 H8 . In the case of mixed-gas experiments, solubility of all components and diffusion coefficients of smaller gasses increase with increasing feed pressure, while diffusion coefficients of higher gasses such as C3 H8 decreases slightly, and this behavior is due to reduction of distance among polymeric matrix segments. Effect of increasing feed pressure on diffusion coefficient of C3 H8 is more significant than that on its solubility coefficient, so permeability of C3 H8 decreases by increasing feed pressure, in contrast to those of CH4 and H2 that exhibit an opposite trend. Although, increasing C3 H8 concentration in feed increases its concentration in the permeate stream, capability of a membrane with certain specific surface area is limited. It means that a membrane which can separate C3 H8 from a C3 H8 concentrated mixture effectively is not able to effectively separate it from a C3 H8 diluted mixture. In other words, performance of a membrane may vary with feed concentration. As a result, increasing C3 H8 concentration to obtain higher permeability is not reasonable. Increasing feed flow rate improves mixing of components in the mixed gas and enhances probability of collision of C3 H8 molecules with the membrane surface. Also, at higher feed flow rate, effect of concentration

In the present investigation, a novel model was developed to predict separation performance of different membranes. The developed model is able to choose the best conditions of preparation for the next membranes heuristically. The model can be easily applied to reduce membrane preparation cost and time, for all types of membranes. In this work, eight different PDMS membranes were synthesized and permeation of a ternary gas mixture (H2 , CH4 and C3 H8 ) through them was studied. PCA and FL were employed to create an interesting method for modeling of the membrane gas separation process. Dimensions of the process were reduced with employing the PCA method. By using this simple method, nearly all effective synthesis parameters, which have not been studied before were considered. FL model was used to predict permeability of C3 H8 , H2 and CH4 in ternary gas mixtures by using a laboratory scale gas separation module equipped with the synthesized PDMS membranes. FL model, based on PCs data bank of the first seven membranes, successfully tracked the permeation behavior of gasses versus temperature, pressure, flow rate, C3 H8 and H2 concentration as well as synthesis parameters of the membranes. This model was then used for prediction of the 8th membrane. Predicting the performance of a membrane, prior to its preparation, was introduced as the most prominent feature of this study. This can offer an intelligent method for synthesis of membranes instead of the time and cost consuming try and error method. Acknowledgements This study was partially supported by Shiraz Oil Refinery Company (Iran, Shiraz) and Iran National Science Foundation (INSF). The authors would like to appreciate Dr. M. Bruetsch, Wacker Silicones Corporation, for supplying silicone oil, crosslinker and catalyst. References [1] S.A. Stern, V.M. Shah, B.J. Hardy, Structure–permeability relationships in silicone polymers, J. Polym. Sci. B: Polym. Phys. 25 (1987) 1263–1298. [2] V.M. Shah, B.J. Hardy, S.A. Stern, Solubility of carbon dioxide, methane, and propane in silicone polymers: effect of polymer side chains, J. Polym. Sci. B: Polym. Phys. 24 (1986) 2033–2047. [3] G.K. Fleming, W.J. Koros, Dilation of polymers by sorption of carbon dioxide at elevated pressures. 1. Silicone rubber and unconditioned polycarbonate, Macromolecules 19 (1986) 2285–2291. [4] T.C. Merkel, V.I. Bondar, K. Nagai, B.D. Freeman, I. Pinnau, Gas sorption, diffusion, and permeation in poly(dimethylsiloxane), J. Polym. Sci. B: Polym. Phys. 38 (2000) 415–434. [5] T.C. Merkel, R.P. Gupta, B.S. Turk, B.D. Freeman, Mixed-gas permeation of syngas components in poly(dimethylsiloxane) and poly(1-trimethylsilyl-1-propyne) at elevated temperatures, J. Membr. Sci. 191 (2001) 85–94. [6] R.S. Prabhakar, T.C. Merkel, B.D. Freeman, T. Imizu, A. Higuchi, Sorption and transport properties of propane and perfluoropropane in

A. Ghadimi et al. / Journal of Membrane Science 360 (2010) 509–521

[7]

[8]

[9]

[10]

[11] [12] [13]

[14]

[15]

[16]

[17] [18]

[19]

[20] [21]

[22]

[23] [24]

[25] [26]

poly(dimethylsiloxane) and poly(1-trimethylsilyl-1-propyne), Macromolecules 38 (2005) 1899–1910. Y. Kamiya, Y. Naito, K. Terada, K. Mizoguchi, A. Tsuboi, Volumetric properties and interaction parameters of dissolved gasses in poly (dimethylsiloxane) and polyethylene, Macromolecules 33 (2000) 3111–3119. R.D. Raharjo, B.D. Freeman, E.S. Sanders, Pure and mixed gas CH4 and n-C4 H10 sorption and dilation in poly(dimethylsiloxane), J. Membr. Sci. 292 (2007) 45–61. R.D. Raharjo, B.D. Freeman, D.R. Paul, G.C. Sarti, E.S. Sanders, Pure and mixed gas CH4 and n-C4 H10 permeability and diffusivity in poly(dimethylsiloxane), J. Membr. Sci. 306 (2007) 75–92. S.H. Choi, J.H. Kim, S.B. Lee, Sorption and permeation behaviors of a series of olefins and nitrogen through PDMS membranes, J. Membr. Sci. 209 (2007) 54–62. C.K. Yeom, S.H. Lee, H.Y. Song, J.M. Lee, Vapor permeations of a series of VOCs/N2 mixtures through PDMS membrane, J. Membr. Sci. 198 (2002) 129–143. F. Wu, L. Li, Z. Xu, S. Tan, Z. Zhang, Transport study of pure and mixed gasses through PDMS membrane, Chem. Eng. J. 117 (2006) 51–59. Y. Shi, C.M. Burns, X. Feng, Poly(dimethyl siloxane) thin film composite membranes for propylene separation from nitrogen, J. Membr. Sci. 282 (2006) 115–123. X. Jiang, A. Kumar, Performance of silicone-coated polymeric membrane in separation of hydrocarbons and nitrogen mixtures, J. Membr. Sci. 254 (2005) 179–188. F. Peng, J. Liu, J. Li, Analysis of the gas transport performance through PDMS/PS composite membranes using the resistances-in-series model, J. Membr. Sci. 222 (2003) 225–234. A. Ghadimi, M. Sadrzadeh, K. Shahidi, T. Mohammadi, Ternary gas permeation through a synthesized PDMS membrane: experimental and modeling, J. Membr. Sci. 344 (2009) 225–236. A. Vecchio, C. Finoli, D. Di Simine, V. Andreoni, Heavy metal biosorption by bacterial cells, Fresenius J. Anal. Chem. 361 (4) (1998) 338–342. M. Shokrian, M. Sadrzadeh, T. Mohammadi, C3 H8 separation from CH4 and H2 using a synthesized PDMS membrane: experimental and neural network modeling, J. Membr. Sci 346 (2010) 59–70. M. Sadrzadeh, A. Ghadimi, T. Mohammadi, Coupling a mathematical and a fuzzy logic-based model for prediction of zinc ions separation from aqueous water using electrodialysis, Chem. Eng. J. 151 (2009) 262–274. H.B. Shen, J. Yang, K.C. Chou, Fuzzy KNN for predicting membrane protein types from pseudo-amino acid composition, J. Theor. Biol. 240 (2006) 9–13. K.V. Kilimann, C. Hartmann, A. Delgado, R.F. Vogel, M.G. Ganzle, A fuzzy logicbased model for the multistage high-pressure inactivation of Lactococcus lactis ssp. cremoris MG 1363, Int. J. Food Microbiol. 98 (2005) 89–105. M.G. Ganzle, K.V. Kilimann, C. Hartmann, R. Vogel, A. Delgado, Data mining and fuzzy modeling of high pressure inactivation pathways of Lactococcus lactis, Innovat. Food Sci. Emerg. Tech. 8 (2007) 461–468. E.I. Tiffee, A. Weber, K. Schmid, V. Krebs, Macroscale modeling of cathode formation in SOFC, Solid State Ionics 174 (2004) 223–232. J.O. Schumacher, P. Gemmar, M. Denneb, M. Zedda, M. Stueber, Control of miniature proton exchange membrane fuel cells based on fuzzy logic, J. Power Sources 129 (2004) 143–151. A. Zilouchian, M. Jafar, Automation and process control of reverse osmosis plants using soft computing methodologies, Desalination 135 (2001) 51–59. D. Hissel, M.C. Pera, J.M. Kauffmann, Diagnosis of automotive fuel cell power generators, J. Power Sources 128 (2004) 239–246.

521

[27] M. Tekin, D. Hissel, M.C. Pera, J.M. Kauffmann, Energy consumption reduction of a PEM fuel cell motor-compressor group thanks to efficient control laws, J. Power Sources 156 (2006) 57–63. [28] D. Lawrence, Handbook of Genetic Algorithms, Van Nostrand Reinhold, 1991. [29] M. Mitchell, An Introduction to Genetic Algorithms, The MIT Press, 1999. [30] G. Winter, J. Periaux, M. Galan, Genetic Algorithms in Engineering and Computer Science, John Wiley & Sons, 1995. [31] Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, Springer-Verlag, 1994. [32] J.S.R. Jang, C.T. Sun, E. Mizutani, Neuro-Fuzzy and Soft Computing: A Computational Approach to Learning and Machine Intelligence, Prentice Hall, Upper Saddle River, NJ, 1997. [33] H. Takagi, I. Hayashi, NN-driven fuzzy reasoning, Int. J. Approx. Reason. 5 (1991) 191–212. [34] J.T. Ross, Fuzzy Logic with Engineering Applications, McGraw Hill, Inc., New York, USA, 1995. [35] C.L. Karr, E.J. Gentry, Fuzzy control of pH using genetic algorithms, IEEE Trans. Fuzzy Syst. 1 (1993) 46–53. [36] Y. Yoshinari, W. Pedrycz, K. Hirota, Construction of fuzzy models through clustering techniques, Fuzzy Set Syst. 54 (1993) 157–165. [37] D. Dubois, H. Prade, Fuzzy Sets and Systems: Theory and Applications, Academic, New York, USA, 1980. [38] T. Takagi, M. Sugeno, Fuzzy identification of systems and its application to modeling and control, IEEE Trans. Syst. Man Cybern. 15 (1985) 116–132. [39] J.S.R. Jang, ANFIS: adaptive network based fuzzy inference system, IEEE Trans. Syst. Man Cybern. 23 (1993) 665–684. [40] D.C. Montgomery, Design and Analysis of Experiments, 5th ed., John Wiley & Sons Inc., NY, 2001. [41] D.R. Cox, N. Reid, The Theory of the Design of Experiments, Chapman & Hall/CRC, Boca Raton, Florida, 2000. [42] L.B. Barrentine, An Introduction to Design of Experiments: A Simplified Approach, ASQ Quality Press, Milwaukee, 1999. [43] A. Dean, D. Voss, Design and Analysis of Experiments, Springer, NY, 1999. [44] K.A. Lokhandwala, R.W. Baker, L.G. Toy, K.D. Amo, Sour Gas Treatment Process Including Dehydration of the Gas Stream, US Patent 5,401,300 (1995). [45] R. Quinn, D.V. Laciak, J.B. Appleby, G.P. Pez, Polyelectrolyte Membranes for the Separation of Acid Gasses, US Patent 5,336,298 (1994). [46] M. Sadrzadeh, M. Amirilargani, K. Shahidi, T. Mohammadi, Pure and mixed gas permeation through a composite polydimethylsiloxane membrane, Polym. Adv. Technol., doi:10.1002/pat.1551. [47] M. Sadrzadeh, K. Shahidi, T. Mohammadi, Effect of operating parameters on pure and mixed gas permeation properties of a synthesized composite PDMS/PA membrane, J. Membr. Sci. 342 (2009) 327–340. [48] M.G. De Angelis, T.C. Merkel, V.I. Bondar, B.D. Freeman, F. Doghieri, G.C. Sarti, Hydrocarbon and fluorocarbon solubility and dilation in poly(dimethylsiloxane): comparison of experimental data with predictions of the Sanchez–Lacombe equation of state, J. Polym. Sci. B: Polym. Phys. 37 (1999) 3011–3026. [49] S.M. Jordan, W.J. Koros, Permeability of pure and mixed gasses in silicone rubber at elevated pressures, J. Polym. Sci.: Part B: Polym. Phys. 28 (1990) 795–809. [50] I. Pinnau, Z. He, Pure- and mixed-gas permeation properties of polydimethylsiloxane for hydrocarbon/methane and hydrocarbon/hydrogen separation, J. Membr. Sci. 244 (2004) 227–233. [51] K.R. Beebe, R.J. Pell, M.B. Seasholtz, Chemometrics: A Practical Guide, John Wiley & Sons, Canada, 1998.