lable at ScienceDirect

Journal of Natural Gas Science and Engineering 15 (2013) 69e75

Contents lists avai

Journal of Natural Gas Science and Engineering

journal homepage: www.elsevier .com/locate/ jngse

Novel methods predict equilibrium vapor methanol content duringgas hydrate inhibition

Mohammad M. Ghiasi a,*, Alireza Bahadori b, Sohrab Zendehboudi c, Ahmad Jamili d,Sina Rezaei-Gomari e

aAhwaz Faculty of Petroleum Engineering, Petroleum University of Technology (PUT), Ahwaz, Iranb School of Environment, Science and Engineering, Southern Cross University, Lismore, New South Wales, AustraliacDepartment of Chemical Engineering, University of Waterloo, Ontario, CanadadMewbourne School of Petroleum and Geological Engineering, The University of Oklahoma, OK, USAe Petroleum Engineering Department, Teesside University, Middlesbrough, UK

a r t i c l e i n f o

Article history:Received 12 May 2013Received in revised form28 August 2013Accepted 25 September 2013Available online

Keywords:Gas hydrateInhibitorMethanol lossCorrelationANN

* Corresponding author. Tel.: þ98 937 76 86 726.E-mail address: mm.ghiasi@gmail.com (M.M. Ghia

1875-5100/$ e see front matter � 2013 Elsevier B.V.http://dx.doi.org/10.1016/j.jngse.2013.09.006

a b s t r a c t

In economic and safety hazards points of view, it is crucial to avoid the formation of clathrate hydrate ofgases in oil and natural gas transportation/production systems. Injection of methanol as a thermody-namic inhibitor is a common approach in industry to shift the hydrate phase boundary to higher pres-sures/lower temperatures. Accurate computation of methanol loss to the vapor phase within hydrateinhibition is essential to calculate the right injection rate of methanol. In this study, two procedures havebeen proposed for fast and precise estimating the ratio of methanol content of vapor phase to methanolliquid composition (RMeOH). In the first method, a new mathematical expression is presented. The ob-tained correlation is reliable for temperatures between 267.15 and 279.15 K and pressures between 1160and 28000 kPa. The second method employs artificial neural network (ANN) approach for RMeOH pre-diction. Both developed models results are in good agreement with reported data in literature. The ANNbased model, however, is more accurate than the new correlation.

� 2013 Elsevier B.V. All rights reserved.

1. Introduction

Gas hydrates, also known as clathrate hydrates, are curious typeof chemical compounds that can be defined as solid solutions(Javanmardi and Moshfeghian, 2000). Combination of water mol-ecules and gas molecules at sufficiently low temperatures and highpressures lead to formation of gas hydrate. Indeed, the watermolecules form a cage like structure wherein gas molecules orguest molecules having suitable sizes are entrapped into the cav-ities (Sloan, 1998). Hydrates exist as three structures (I, II, and H)depending on how many water molecules incorporate the funda-mental building blocks (Pellenbarg and Max, 2000) and gas mole-cule size (Ghiasi, 2012). Structure I is formed from small gasmolecules such as methane. Larger molecules such as propane orbutane form structure II. Such gases as Xe and Ar are capable offorming both I and II structures (Nasrifar and Moshfeghian, 2001;Ghiasi and Mohammadi, 2013). Formation of type H hydrate re-quires a small molecule in addition to the type H former such as

si).

All rights reserved.

adamantine or methylcyclopentane. In natural gas type H formersare not generally available (Caroll, 2009). More detailed descriptionof structure H can be found elsewhere (Mehta and Sloan, 1994).

Hydrates can be used as proper approach for gas separation andpurification and CO2 capture (Duc et al., 2007; Kang and Lee, 2000;Kumar et al., 2006), gas transmission and storage (Javanmardi et al.,2005; Jeon et al., 2006), water sweetening (Javanmardi andMoshfeghian, 2003), and refrigeration and air conditioning sys-tems (Fournaison et al., 2004). Stored gas in the earth as gas hydratereservoirs can be considered as future source of energy (Chattiet al., 2005; Englezos, 1993; Milkov and Sassen, 2002). Formationof hydrates in oil and gas transmission/production systems, how-ever, results in pipeline blockage and irreparable damages toequipment. Hence, to avoid economic risks and safety hazards it isof great importance to prevent hydrate formation. Dehydration ofnatural gas eliminates the possibility of condensed water forma-tion. Consequently, the formation of gas hydrate is not probable.Albeit the gas dehydration is permanent solution to avoid hydrateformation, usually this process is not considered to be actually/economically feasible (Bahadori and Vuthaluru, 2010). In the casesof not having bone dry gas, holding the operating conditions ofpipeline out of hydrate stability zone by insulation of pipeline or by

M.M. Ghiasi et al. / Journal of Natural Gas Science and Engineering 15 (2013) 69e7570

active heating is substitute for eschewing hydrate formation. Morepractical option, however, is injection of hydrate inhibitors to ruleout the hydrate formation. The commonly used inhibitors in theindustry are alcohols, especially methanol (Bahadori andVuthaluru, 2009; Elgibaly and Elkamel, 1999).

Methanol or methyl alcohol is an aliphatic alcohol and known asa highly polar molecule. This small molecule interacts strongly withother fluids in an H-bonded network (Simonson et al., 1987). Hence,mixtures having methanol as one of the components show someanomaly (Bands et al., 1982; Marcus, 1999; Staib, 1998). Methanol isone of the most frequently used chemical compounds in variousindustries. It can be used as a basic feedstock for plastic manufac-ture (Mokhatab et al., 2006) and also can be employed as analternative fuel for gasoline cars (Matar, 2000). Since methanol hashigh reactivity, it could be used for production of many chemicals(Chang, 1984). Industrial usages of methanol have been describedelsewhere (Machado and Streett, 1983). As a thermodynamic in-hibitor, methanol shifts hydrate formation conditions to lowertemperatures/higher pressures by reducing water activity. Ham-merschmidt (Caroll, 2009) proposed the following equation to es-timate the effect of methanol on hydrate formation temperature:

DT ¼ 1297WMð100�WÞ (1)

where DT is the temperature depression in K; M is molecularweight of methanol in g/mol; and W is methanol concentration inliquid water in wt%.

In 2005, Østergaard et al. (2005) developed another equation forcalculation of various salts and alcohols effect on hydrate formationtemperature. Correlation of Østergaard et al. (2005) is as follows:

DT ¼�c1W þ c2W

2 þ c3W3�ðc4lnðPÞ þ c5Þðc6ðP0 � 1000Þ þ 1Þ

(2)

where ci are constants; P is pressure in kPa; and P0 is Dissociationpressure of hydrocarbon fluid in the presence of distilled water at273.15 K in kPa.

In addition to the available empirical and semi-empirical cor-relations, thermodynamic models are also presented by some au-thors such as Nasrifar and Moshfeghian (2001), Nasrifar andMoshfeghian (2001), Tavasoli et al. (2011) and Tavasoli et al.(2011) to compute the hydrate formation temperature in thepresence of alcohols. The calculated amount of methanol by thesemodels for injection in pipelines, however, is only sufficient toprevent freezing of the inhibitor water phase. Indeed, the injectionrate of methanol must be adequate so that it provides the methanolvapor loss, methanol loss to the hydrocarbon liquid phase, andrequiredmethanol concentration in liquid water. It should be notedthat methanol is only fruitful in liquid water phase; hence, thedissolved methanol in vapor and liquid hydrocarbon phases isconsidered as losses (Bruinsma et al., 2004). The injected methanolas hydrate inhibitor, however, causes many problems for glycoldehydration plants (Gue and Ghalambor, 2005). From environ-mental point of view, the ventedmethanol vapor from regenerationsystem to the atmosphere is hazardous and should be recovered(Gue and Ghalambor, 2005). In addition, the operating expenserelated with the lost methanol cost will be decreased by regener-ation of methanol. So, calculation of methanol vapor loss is crucialfor both hydrate calculations and methanol regeneration systemdesign.

In order to compute the equilibrium methanol vapor contentwithin gas hydrate inhibition, a proper equation of state (EoS) couldbe used. It should be noted that finding a convenient EoS for the

system of interest is a true challenge (Orbey and Sandler, 1998;Poling et al., 2004). It is believed that cubic equations of state likePR EoS (Peng and Robinson, 1976) and SRK EoS (Soave, 1972) givegood results for non-polar mixtures and slightly polar systems(Asselineau et al., 1978; Graboski and Daubert, 1978; Huron et al.,1977). Nevertheless, in the case of polar system, the estimationsare poor. Types of equations of state presented by Chapman et al.(Chapman et al., 1989, 1990, 1988) and Huang and Radosz (1990)based on Wertheim’s theory, i.e. statistical associating fluid the-ory (SAFT) equations of state, is precise for pure fluids andmixturesconsisting associating fluids. SAFT EoS suffers from complexity(Haghighi, 2009). To avoid sophisticate calculations, combination ofthe association term from SAFT with a cubic EoS has been proposedin the literature (Haghighi, 2009). These models are known as CPAwhich indicates cubic plus association.

The main objective of this work is to present novel methods foraccurate and fast prediction of methanol vapor loss within hydrateinhibition. First, a new analytical expression will be developed forRMeOH prediction. Next amongst available artificial neural networks(ANNs) the proper network and the best topology for selectednetworkwill be found for the application of interest. Using this typeof computational intelligences has been proven to give excellentresults in the case of natural gas hydrate modeling (Elgibaly andElkamel, 1998; Ghiasi and Ghayyem, in press; Zahedi et al., 2009).Applying ANN for RMeOH prediction is new based on our literaturesurvey. The final section presents comparison of developed ANNmodel and the obtained correlation results based on average ab-solute deviation percent (AAD %).

2. Proposed methods

2.1. Development of statistical model

With the aim of developing a simple to use correlation capableto predict the methanol loss in vapor phase within hydrate in-hibition accurately, first, 326 data points have been collectedfrom reliable source (GPSA, 2004). Next, the ratio of methanolcontent of vapor phase to methanol liquid composition, asdefined by Equation (3), is assumed to be function of temperatureand pressure.

RMeOH ¼kg MeOH

MSm3 Natural GasWt% MeOH in Water Phase

(3)

The final step is finding a proper approximate function for theapplication of interest. The approximant does not need to passthrough all the points. It is necessary, however, that this functionmark out the data points as a whole with the smallest error (Yanget al., 2005). Amongst most commonly used approximantsinclude trigonometric functions, exponential functions, and poly-nomials (Hoffman, 2001), the last one is widely used for treatingwith functions on finite domains. Weierstrass approximation the-orem (Burkill, 1959; Hoffman, 2001) could be defined as a suitablereason for usage advantageous of polynomials. In this study, abivariate polynomial of the form of Equation (4) is selected torepresent the dependent and independent variables.

z ¼ a0 þ a1xþ a2yþ a3x2 þ a4y

2 þ a5xyþ a6x3 þ a7y

3 þ a8x2y

þ a9xy2

(4)

The final correlation for estimation of methanol vapor loss found tobe as follows:

Table 1Tuned coefficients used in Equation (5) for estimation of RMeOH.

Coeff. Value Coeff. Value Coeff. Value

A1 1860.221107545160 B1 1686664.19330012 C1 �15130.2481920805A2 �6.789273735858360 B2 573061984.439538 C2 33.1836622752203A3 0.008260794455384 B3 �21970996769.4559 C3 �2000951.15194788

D �169912.225980511

M.M. Ghiasi et al. / Journal of Natural Gas Science and Engineering 15 (2013) 69e75 71

RMeOH ¼�A1T þA2T

2þA3T3�þ�B1

�1P

�þB2

�1P

�2þB3

�1P

�3�

þ�C1T �

�1P

�þC2T

2��1P

�þC3T �

�1P

�2�þD

(5)

where T is temperature in K, P is pressure in kPa, and Ai, Bi, Ci, and Dare coefficients.

All gathered data points were employed in a multi-regressionprocedure in order to optimize the values of the constants andminimizing the errors between predicted and experimental values.Tuned coefficients of the proposed correlation are tabulated inTable 1.

2.2. Development of ANN model

ANNs are considered as another approach at modeling the in-formation processing capabilities of nervous systems (Rojas, 1996)that primarily used for pattern recognition, classification, andprediction (Bose and Liang, 1996; Haykin, 1999). This technique aswell as genetic algorithms and fuzzy systems attract more andmore consideration in various research fields as they tolerate awide range of uncertainty (Jin and Jiang, 1999). Employment of amassive interconnection of neurons as simple computing cells inneural networks will contribute to attain excellent performance. Atypical model of an artificial neuron is shown in Fig. 1. Mathemat-ically a neuronm could be represented by the following equations:

rm ¼Xni¼1

ðwmixi þ bmÞ (6)

ym ¼ f ðrmÞ (7)

where x1, x2,.,xn are the input signals (scalar); wm1, wm2,., wmnare the neuron’s synaptic weights; rm is the linear combiner

Fig. 1. Mathematical model

output; bm is the bias term; f is the activation function; and ym isthe output signal of the neuron. It should be noted that the biasterm may not be employed depending on the situation.

Among several types of available neural networks include feed-forward neural networks (FFNNs), recurrent neural networks(RNNs), and self-organizing maps (SOMs), FFNNs are most power-ful, versatile, and reliable non-linear classifier recognizer (Looney,1997). May be the multiple-layered perceptron (MLP), amidst allother FFNNs, is the most popular network architecture that used bychemical, petroleum and natural gas engineers. In this study a MLPnetwork is employed for estimation of methanol vapor loss withinhydrate inhibition. Due to the fact that the standard multilayerFFNNs with as few as one hidden layer is capable to approximateany piecewise continuous function at certain conditions (Horniket al., 1989), number of hidden layers is assumed to be one. Fig. 2represents a three-layered MLP with I input branching nodes, Hhidden neurons, and O output neurons. In this work, RMeOH isoutput of the desired network and temperature and pressure areinputs. Hence, I and O are equal to 2 and 1, respectively. To definethe number of hidden neurons,H, Themean squared error (MSE), asdefined by Equation (8), and regression R-value are chosen ascriteria for performance evaluation.

MSE ¼ 1n

Xni¼1

ðti � oiÞ2 (8)

where n is number of the points, ti is experimental RMeOH (target),and oi is the calculated RMeOH (output of the network).

The input neurons transmit temperature and pressure to theneurons of the hidden layer. By performing a weighted summationof outputs of input layer, the inputs of the hidden layer will bedetermined. The output of hidden layer, which is also the input ofoutput layer, is calculated by transferring its input employing anon-linear transfer function. Finally, RMeOH is computed by trans-ferring the input of output layer using linear transfer function. Thelog-sigmoid transfer function is used in hidden layer. This transfer

of an artificial neuron.

Fig. 2. A typical three-layered ANN with one hidden layer.

M.M. Ghiasi et al. / Journal of Natural Gas Science and Engineering 15 (2013) 69e7572

function generates outputs between 0 and 1 and is expressed by thefollowing equation:

f ðxÞ ¼ 11þ expð�xÞ (9)

With regard to the output and target values differences, the ANNmodel adjusts the values of synaptic weights between computingcells such that the outputs approach targets. To train the network asuitable learning algorithm is needed. In 1949, Hebb (Hebb, 1949)presented a learning scheme based on pre and post synaptic valuesof the variable. Hebb’s rule is the oldest learning law. Nowadays,there are many learning laws most of which are some sort of the

Fig. 3. Correlation analysis between network predictions and the correspondingtargets.

Hebb’s rule. In the present work, the most practical learning algo-rithm, i.e. back-propagation, is used. By using this algorithm, theerrors following from output and target values differences willpropagate backward via the network, and the weight valuesadjusted so that error minimizes. Since the LevenbergeMarquardt(LM) method provides the best generalization performance, theback-propagation algorithm is trained with LM. Detail descriptionof LM method can be found elsewhere (Kelley, 1999; Nocedal andWright, 1999; Press et al., 1992).

Before training the network, the collected data points fromGPSA (2004) were normalized and then separated into threegroups, randomly: training set, testing set, and validation set. Thetraining set including 50% of the data is used to fit the weights ofthe network, while the validation set indicates the network per-formance after training. The evaluation of created model is per-formed by testing set. Each of the validation and testing setscomprise 25% of the collected data.

3. Results and discussion

3.1. Structure of developed ANN model

The remaining task was finding the optimum number of thehidden neurons. As mentioned before, the criterion for selection ofbest structure is lowest MSE as well as suitable regression R-value.With a 2-H-1 structure, H was varied from 1 to 25 and the perfor-mance of network in prediction of methanol loss in vapor phasewas measured. The results are demonstrated in Figs. 3 and 4. As canbe seen from Fig. 3, it can be concluded that using hidden neuronsmore than 5 give no further improvement in R-value. AnalyzingFig. 4 which gives MSE versus number of hidden neurons, however,confirms that using hidden neurons equal to 14 provides minimumerror between the network predictions and target values. Hence,the optimum topology is 2-14-1. The precision of developed neuralbase model results is shown in Fig. 5.

3.2. Comparison of proposed models

The objective of this part is to evaluate the accuracy of con-structed ANN model in predicting methanol vapor loss in com-parison with new empirical correlation. The average absolutedeviation percent (AAD %), as defined in Equation (10), is employedto check the estimation capability of proposed models. AAD % equal

Fig. 4. Performance evaluation of various ANN structures based on MSE.

Calculated RMeOH

10 15 20 25 30 35 40

Exp

erim

enta

l RM

eOH

10

15

20

25

30

35

40

R-value = 0.999

Fig. 5. Experimental values of RMeOH versus outputs of developed ANN model.

Table 3The predictions of new models in comparison with some extracted data form GPSA(2004), T ¼ 273.15 K.

GPSA (2004) ANN model New correlation

Pressure, kPa RMeOH RMeOH AD % RMeOH AD %

7065.81 1209 12.03 0.46 12.64 4.565883.58 13.31 13.28 0.22 13.67 2.705439.54 13.91 13.87 0.24 14.18 1.994996.22 14.54 14.56 0.19 14.79 1.784559.13 15.36 15.37 0.04 15.52 1.034106.21 16.36 16.38 0.16 16.45 0.583746.98 17.32 17.36 0.22 17.36 0.253464.19 18.24 18.26 0.09 18.22 0.143181.86 19.30 19.32 0.09 19.23 0.362961.02 20.36 20.29 0.37 20.17 0.942755.5 21.36 21.32 0.17 21.18 0.812581.08 22.28 22.32 0.16 22.17 0.502433.55 23.28 23.27 0.02 23.12 0.682294.46 24.27 24.27 0.00 24.12 0.602163.32 25.30 25.32 0.08 25.19 0.441935.71 27.45 27.43 0.06 27.35 0.361743.41 29.57 29.58 0.02 29.57 0.011570.22 31.72 31.83 0.43 31.95 0.731499.96 32.81 32.90 0.25 33.03 0.671442.25 33.87 33.80 0.20 33.97 0.301333.4 35.73 35.66 0.18 35.88 0.42

Table 4

M.M. Ghiasi et al. / Journal of Natural Gas Science and Engineering 15 (2013) 69e75 73

to 1.30% proves that the new correlation can be used successfullyfor fast estimation of RMeOH. The used experimental data weregenerated by the neural-based model with AAD % equal to 0.27%.Hence, the predictions of neural network based model are in betteragreement with reported data in GPSA (2004). Hence, applyingANN as computational intelligence for RMeOH prediction gives morereliable results in comparison with presented mathematicalexpression.

AAD% ¼ 100X����ðti � oiÞ

ti

����=n (10)

Estimated methanol vapor composition to the methanol liquidcomposition using developed models in comparison with experi-mental data at 269.15 K, 273.15 K, and 277.15 K can be found inTables 2e4, respectively. Fig. 6 demonstrates the obtained results

Table 2The predictions of new models in comparison with some extracted data form GPSA(2004), T ¼ 269.15 K.

GPSA (2004) ANN model New correlation

Pressure, kPa RMeOH RMeOH AD % RMeOH AD %

4529.41 12.02 12.08 0.47 11.48 4.494160.27 12.71 12.73 0.15 12.08 4.993796.31 13.44 13.50 0.41 12.80 4.753486.92 14.27 14.27 0.00 13.56 5.003181.86 15.20 15.18 0.11 14.46 4.822884.57 16.26 16.26 0.01 15.56 4.282649.48 17.25 17.29 0.22 16.62 3.632465.59 18.18 18.24 0.33 17.61 3.102324.67 19.11 19.07 0.18 18.49 3.222177.51 20.07 20.05 0.05 19.53 2.662053.06 21.09 21.00 0.44 20.54 2.621935.71 22.09 22.00 0.41 21.61 2.151849.1 23.01 22.81 0.88 22.49 2.281743.41 24.00 23.90 0.42 23.67 1.381654.55 25.00 24.92 0.31 24.78 0.861580.52 25.86 25.84 0.06 25.80 0.251490.19 26.95 27.08 0.46 27.15 0.711377.72 28.64 28.79 0.53 29.02 1.331324.71 29.60 29.68 0.27 29.99 1.30

from the constructed ANN model and new correlation for RMeOH asa function of pressure at 267.15 K, 271.15 K, 275.15 K, and 279.15 K,respectively.

4. Summery and conclusion

In this work, two procedures proposed for accurate prediction ofratio of methanol content of vapor phase to methanol liquidcomposition. Both developed models are based on extracted datafrom GPSA (2004). The collected data cover temperatures between267.15 K and 279.15 K, and pressures between 1162.31 kPa and28127 kPa. In the first method, a mathematical expression pre-sented that describes RMeOH as function of temperature and

The predictions of new models in comparison with some extracted data form GPSA(2004), T ¼ 277.15 K.

GPSA (2004) ANN model New correlation

Pressure, kPa RMeOH RMeOH AD % RMeOH AD %

17099.8 12.12 12.10 0.14 11.81 2.5413726.1 12.58 12.57 0.01 12.45 1.0611089.5 13.24 13.23 0.11 13.22 0.159075.98 14.07 14.08 0.03 14.13 0.416655.06 15.96 15.91 0.32 15.97 0.075885.96 16.89 16.84 0.25 16.88 0.025205.73 17.88 17.92 0.23 17.92 0.234664.03 18.97 19.01 0.20 18.97 0.023866.83 21.09 21.16 0.34 21.06 0.153578.24 22.11 22.17 0.25 22.05 0.323311.19 23.14 23.26 0.49 23.11 0.123083.94 24.17 24.32 0.63 24.17 0.002872.29 25.30 25.46 0.65 25.30 0.002727.54 26.30 26.34 0.06 26.17 0.592427.97 28.51 28.47 0.13 28.28 0.822320.56 29.40 29.36 0.14 29.15 0.842217.91 30.40 30.29 0.35 30.07 1.082119.8 31.32 31.25 0.23 31.01 1.002039.16 32.25 32.10 0.45 31.85 1.251936.4 33.24 33.28 0.11 33.00 0.751862.74 34.30 34.19 0.32 33.88 1.231780.34 35.30 35.29 0.02 34.94 1.01

RMeOH

10 15 20 25 30 35 40

Pres

sure

, kPa

103

104

105

Exp Data, T=267.15 KExp Data, T=271.15 KExp Data, T=275.15 KExp Data, T=279.15 KANN modelNew correlation

Fig. 6. Results of proposed models for RMeOH prediction in comparison with reporteddata in GPSA (2004).

M.M. Ghiasi et al. / Journal of Natural Gas Science and Engineering 15 (2013) 69e7574

pressure. The experimental data were reproduced with an AAD % of1.30% by using the obtained correlation. Good performance of newcorrelation for RMeOH prediction along with its simplicity makes itas useful tool for any industrial applications.

In the secondmethod, ANN approach was employed to estimateRMeOH. A standard two-layer feed-forward back-propagation neuralnetwork trained with LM was selected as appropriate network. Tofind the optimum number of neurons in the hidden layer, the cri-terionwas regression R-value andMSE between the target data andnetwork outputs. Finally 2-14-1 topology founds to be the beststructure for network. All gathered data was regenerated by theneural network based model with an AAD % equal to 0.26%. Hence,ANN as computational intelligence provides much better results incomparison with new proposed correlation. The new empiricalcorrelation, though less accurate than the neural-based model,provides more simplicity for hand calculations.

List of symbols

ai, Ai CoefficientAAD % Average absolute deviation percentANN Artificial neural networkBi Coefficientbm Bias termci, Ci CoefficientCPA Cubic plus associationD CoefficientEoS Equation of statef Activation functionFFNN Feed-forward neural networkH Hidden neuronsI Input branching nodesLM LevenbergeMarquardtM Molecular weight of methanol in g/molMeOH MethanolMLP Multiple-layered perceptronMSE Mean squared errorn Number of pointsO Output neuronsoi Calculated RMeOHP Pressure (kPa)

P0 Dissociation pressure of hydrocarbon fluid in thepresence of distilled water at 273.15 K (kPa)

RMeOH Ratio of methanol content of vapor phase to methanolliquid composition

rm Linear combiner outputRNN Recurrent neural networkSAFT Statistical associating fluid theorySOM Self-organizing mapT Temperature (K)ti Experimental RMeOHW Methanol concentration in liquid water in wt%.wmi Neuron’s synaptic weightsxi Input signalsym Output signal of the neuronDT Temperature depression in K

References

Asselineau, L., Bogdani�c, G., Vidal, J., 1978. Calculation of thermodynamic propertiesand vapor-liquid equilibria of refrigerants. Chem. Eng. Sci. 33 (9), 1269e1276.

Bahadori, A., Vuthaluru, H.B., 2009. A novel correlation for estimation of hydrateforming condition of natural gases. J. Nat. Gas Chem. 18, 453e457.

Bahadori, A., Vuthaluru, H.B., 2010. Prediction of methanol loss in vapor phaseduring gas hydrate inhibition using Arrhenius-type functions. J. Loss Prev.Process Ind. 23, 379e384.

Bands, R., Kabisch, G., Pollmer, K., 1982. Hydrogen bonding in methanoldorganicsolvent and methanoldwater mixtures as studied by the vco and voh. J. Mol.Struct. 81 (1e2), 35e50.

Bose, N.K., Liang, P., 1996. Neural Network Fundamentals with Graphs, Algorithms,and Applications. In: McGRaw-Hill Series in Electrical and Computer Engi-neering. McGraw-Hill, USA.

Bruinsma, D.F.M., Desens, J.T., Notz, P.K., Sloan, E.D., 2004. A novel experimentaltechnique for measuring methanol partitioning between aqueous and hydro-carbon phases at pressures up to 69 MPa. Fluid Phase Equilib. 222e223 (0),311e315.

Burkill, J.G., 1959. Lectures on Approximation by Polynomials. Tata Institute ofFundamental Research, Bombay.

Caroll, J., 2009. Natural Gas Hydrate, a Guide for Engineers. Gulf Professional Pub-lishing, USA.

Chang, C.D., 1984. Methanol conversion to light olefins. Catal. Rev. Sci. Eng. 26,323e345.

Chapman, W.G., Gubbins, K.E., Jackson, G., Radosz, M., 1989. SAFT: equation-of-statesolution model for associating fluids. Fluid Phase Equilib. 52 (0), 31e38.

Chapman, W.G., Gubbins, K.E., Jackson, G., Radosz, M., 1990. New reference equationof state for associating liquids. Ind. Eng. Chem. Res. 29 (8), 1709e1721.

Chapman, W.G., Jackson, G., Gubbins, K.E., 1988. Phase equilibria of associatingfluids. Mol. Phys. 65 (5), 1057e1079.

Chatti, I., Delahaye, A., Fournaison, L., Petitet, J.P., 2005. Benefits and drawbacks ofclathrate hydrates: a review of their areas of interest. Energy Convers. Manag.46 (9e10), 1333e1343.

Duc, H.N., Chauvy, F., Herri, J.M., 2007. CO2 capture by hydrate crystallization e apotential solution for gas emission of steelmaking industry. Energy Convers.Manag. 48 (4), 1313e1322.

Elgibaly, A., Elkamel, A., 1998. A new correlation for predicting hydrate formation con-ditions for various gas mixtures and inhibitors. Fluid Phase Equilib. 152, 23e42.

Elgibaly, A., Elkamel, A., 1999. Optimal hydrate inhibition policies with the aid ofneural networks. Energy Fuels 13, 105e113.

Englezos, P., 1993. Clathrate hydrates. Ind. Eng. Chem. Res. 32 (7), 1251e1274.Fournaison, L., Delahaye, A., Chatti, I., Petitet, J.P., 2004. CO2 hydrates in refrigeration

processes. Ind. Eng. Chem. Res. 43 (20), 6521e6526.Ghiasi, M.M., 2012. Initial estimation of hydrate formation temperature of

sweet natural gases based on new empirical correlation. J. Nat. Gas Chem. 21,508e512.

Ghiasi, M.M., Ghayyem, M.A. Application of artificial neural network (ANN) inprediction of hydrate formation temperature. Energy Source Part A (in press).

Ghiasi, M.M., Mohammadi, A.H., 2013. Determination of methane-hydrate phaseequilibrium in the presence of electrolytes or organic inhibitors by using asemi-theoretical framework. Energy Technol 1 (9), 519e529.

GPSA, 2004. Gas Processors Suppliers Association, USA.Graboski, M.S., Daubert, T.E., 1978. A modified soave equation of state for phase

equilibrium calculations. 2. Systems containing CO2, H2S, N2, and CO. Ind. Eng.Chem. Process Design Dev. 17 (4), 448e454.

Gue, B., Ghalambor, A., 2005. Natural Gas Engineering Handbook. Gulf ProfessionalPublishing, USA.

Haghighi, H., 2009. Phase Equilibria Modelling of Petroleum Reservoir Fluids Con-taining Water, Hydrate Inhibitors and Electrolyte Solutions. Heriot-Watt Uni-versity, Scotland, UK.

Haykin, S.S., 1999. Neural Networks: a Comprehensive Foundation. Prentice HallInternational.

M.M. Ghiasi et al. / Journal of Natural Gas Science and Engineering 15 (2013) 69e75 75

Hebb, D.O., 1949. The Organization of Behavior: a Neuropsychological Theory. JohnWiley and Sons, Inc., USA.

Hoffman, J.D., 2001. Numerical Methods for Engineers and Scientists. Marcel Dek-ker, Inc., USA.

Hornik, K., Stinchcombe, M., White, H., 1989. Multilayer feedforward networks areuniversal approximators. Neural Netw. 2 (5), 359e366.

Huang, S.H., Radosz, M., 1990. Equation of state for small, large, polydisperse andassociating molecules. Ind. Eng. Chem. Res. 29, 2284e2294.

Huron, M.-J., Dufour, G.-N., Vidal, J., 1977. Vapour-liquid equilibrium and criticallocus curve calculations with the soave equation for hydrocarbon systems withcarbon dioxide and hydrogen sulphide. Fluid Phase Equilib. 1 (4), 247e265.

Javanmardi, J., Moshfeghian, M., 2000. A new approach for prediction of gas hydrateformation conditions in aqueous electrolyte solutions. Fluid Phase Equilib. 168,135e148.

Javanmardi, J., Moshfeghian, M., 2003. Energy consumption and economic evalua-tion of water desalination by hydrate phenomenon. Appl. Therm. Eng. 23 (7),845e857.

Javanmardi, J., Nasrifar, K., Najibi, S.H., Moshfeghian, M., 2005. Economic evaluationof natural gas hydrate as an alternative for natural gas transportation. Appl.Therm. Eng. 25, 1708e1723.

Jeon, Y.H., et al., 2006. A study of the kinetics characteristics of natural gas hydrate.J. Ind. Eng. Chem. 12 (5), 733e738.

Jin, Y., Jiang, J., 1999. Techniques in neural-network based fuzzy system identifica-tion and their application to control of complex systems. In: Leondes, C.T. (Ed.),Fuzzy Theory Systems, Techniques and Applications. Academic Press, USA.

Kang, S.P., Lee, H., 2000. Recovery of CO2 from flue gas using gas hydrate: ther-modynamic verification through phase equilibrium measurements. Environ.Sci. Technol. 34, 4397e4400.

Kelley, C.T., 1999. Iterative Methods for Optimization. SIAM Press, USA.Kumar, R., Wu, H., Englezos, P., 2006. Incipient hydrate phase equilibrium for gas

mixtures containing hydrogen, carbon dioxide and propane. Fluid Phase Equi-lib. 244 (2), 167e171.

Looney, C.G., 1997. Pattern Recognition Using Neural Networks, Theories and Al-gorithms for Engineers and Scientists. Oxford University Press, USA.

Machado, J.R.S., Streett, W.B., 1983. Equation of state and thermodynamic propertiesof liquid methanol from 298 to 489 K and pressures to 1040 bars. J. Chem. Eng.Data 28 (2), 218e223.

Marcus, Y., 1999. Preferential solvation in mixed solvents Part 8. Aqueous methanolfrom sub-ambient to elevated temperatures. Phys. Chem. Chem. Phys. 1 (12),2975e2983.

Matar, S., 2000. Chemistry of Petrochemical Processes. Gulf Professional Company,USA.

Mehta, A.P., Sloan, E.D., 1994. A thermodynamic model for structure-H hydrates.AIChE J. 40 (2), 312e320.

Milkov, A., Sassen, R., 2002. Economic geology of offshore gas hydrates accumula-tions and provinces. Mar. Pet. Geol. 19 (1), 1e11.

Mokhatab, S., Poe, W.A., Speight, J.G., 2006. Handbook of Natural Gas Transmissionand Processing. Gulf Professional Publishing, USA.

Nasrifar, K., Moshfeghian, M., 2001. A model for prediction of gas hydrate formationconditions in aqueous solutions containing electrolytes and/or alcohol. J. Chem.Thermodyn. 33, 999e1014.

Nocedal, J., Wright, S.J., 1999. Numerical Optimization. Springer Publishing Com-pany, USA.

Orbey, H., Sandler, S.I., 1998. Modeling Vapor-liquid Equilibria; Cubic Equations ofState and Their Mixing Rules. Cambridge University Press, Cambridge.

Østergaard, K.K., Masoudi, R., Tohidi, B., Danesh, A., Todd, A.C., 2005. A generalcorrelation for predicting the suppression of hydrate dissociation tem-perature in the presence of thermodynamic inhibitors. J. Pet. Sci. Eng. 48,70e80.

Pellenbarg, R.E., Max, M.D., 2000. Introduction, physical properties, and naturaloccurrences of hydrate. In: Max, M.D. (Ed.), Natural Gas Hydrate in Oceanic andPermafrost Environments. Kluwer Academic Publishers, Dordrecht, TheNetherlands, pp. 1e8.

Peng, D.-Y., Robinson, D.B., 1976. A new two-constant equation of state. Ind. Eng.Chem. Fundam. 15 (1), 59e64.

Poling, B.E., Prausnitz, J.M., O’Connell, J.P., 2004. The Properties of Gases and Liquids.McGraw Hill Book Company, New York.

Press, W.H., Teukolsky, S.A., Vetterling, A.W.T., Flannery, B.P., 1992. NumericalRecipes in C: the Art of Scientific Computing. Cambridge University Press,USA.

Rojas, R., 1996. Neural Networks, a Systematic Introduction. Springer PublishingCompany, Berlin.

Simonson, J.M., Bradley, D.J., Busey, R.H., 1987. Excess molar enthalpies and thethermodynamics of (methanol þ water) to 573 K and 40 MPa. J. Chem. Ther-modyn. 19, 479e492.

Sloan, E.D., 1998. Clathrate Hydrates of Natural Gases. Marcel Dekker, Inc., USA.Soave, G., 1972. Equilibrium constants from a modified Redlich-Kwong equation of

state. Chem. Eng. Sci. 27 (6), 1197e1203.Staib, A., 1998. Theoretical study of hydrogen bond dynamics of methanol in so-

lution. J. Chem. Phys. 108 (11), 4554e4563.Tavasoli, H., Feyzi, F., Dehghani, M.R., Alavi, F., 2011. Prediction of gas hydrate for-

mation condition in the presence of thermodynamic inhibitors with the ElliotteSuresheDonohue equation of state. J. Pet. Sci. Eng. 77, 93e103.

Yang, W.Y., Cao, W., Chung, T.S., Morris, J., 2005. Applied Numerical Methods UsingMatlab. John Wiley & Sons, Inc., USA.

Zahedi, G., Karami, Z., Yaghoobi, H., 2009. Prediction of hydrate formation tem-perature by both statistical models and artificial neural network approaches.Energy Convers. Manag. 50.