Theoretical and experimental study of phase equilibrium of semi-clathrate hydrates of methane + tetra-n-butyl-ammonium bromide aqueous solution

Accepted Manuscript Theoretical and experimental study of phase equilibrium of semi-clathrate hydrates of methane + tetra-n-butyl-ammonium bromide aqueous solution Hesam Najibi, Kamalodin Momeni, Mohammad T. Sadeghi PII:

S1875-5100(15)30248-1

DOI:

10.1016/j.jngse.2015.11.002

Reference:

JNGSE 1098

To appear in:

Journal of Natural Gas Science and Engineering

Received Date: 18 July 2015 Revised Date:

31 October 2015

Accepted Date: 2 November 2015

Please cite this article as: Najibi, H., Momeni, K., Sadeghi, M.T., Theoretical and experimental study of phase equilibrium of semi-clathrate hydrates of methane + tetra-n-butyl-ammonium bromide aqueous solution, Journal of Natural Gas Science & Engineering (2015), doi: 10.1016/j.jngse.2015.11.002. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Theoretical and experimental study of phase equilibrium of semiclathrate hydrates of methane + tetra-n-butyl-ammonium bromide aqueous solution Hesam Najibia,*, Kamalodin Momenia, Mohammad T. Sadeghib a b

Faculty of Petroleum Engineering, Petroleum University of Technology (PUT), Ahwaz, Iran, Post Box: 63431 Department of Chemical Engineering, Iran University of Science and Technology (IUST), Tehran, Iran

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Abstract – In this study, the phase stability conditions of semi-clathrate hydrate of methane + tetra-n-butyl-ammonium bromide (TBAB) + water system is investigated. New experimental

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data on the hydrate-liquid-vapor equilibrium conditions of this system is measured. The measured data is for the pressure range of 2.88 to 14.1 MPa, temperature range of 285.6 to 295.9 K and TBAB mass fractions of 0.05, 0.15 and 0.3. A thermodynamic model is also developed to predict the phase stability conditions of hydrate for this system. In the developed model, the phase equilibrium of the hydrate of pure TBAB in water is predicted based on the Gibbs free energy minimization technique. This model is then combined with the statistical thermodynamic

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model of van der Waals–Platteeuw (vdW–P) to predict the phase stability conditions of semiclathrate hydrate of methane with TBAB in aqueous solution. Binding mean spherical approximation (BiMSA) electrolyte model is used for aqueous phase properties prediction and modified Peng–Robinson equation of state (PR-EoS) is used for calculation of the gaseous phase

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properties. The results show that the developed model satisfactorily predicts the experimental data with Average Absolute Relative Deviation (AARD) of 12%. Moreover, the model is able to

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predict the different types of pure TBAB semi-clathrate hydrates and also the inhibition and promotion effects of this salt. The results also show that considering the association effect in the electrolyte model, can improve the predictions of the developed thermodynamic model for hydrate phase equilibrium of methane in the presence of TBAB aqueous solution.

Keywords: Semi-clathrate hydrate; TBAB; Methane; Thermodynamic model; BiMSA. *Corresponding author: Tel/Fax: +98 613 5551754. E-mail address: [email protected], [email protected]

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1. Introduction Clathrate hydrates are non-stoichiometric compounds composed of hydrogen bounded

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lattice structures made by water molecules and small gas molecules trapped in the cages of the lattice. Production and accumulation of hydrates in oil and gas processing/transportation facilities can block the pipeline and cause serious damages (Najibi et al., 2006; Sloan and Koh,

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2008). In the last two decades clathrate hydrates are considered as a suitable media for natural gas storage and transportation (Gudmundsson, 1996; Najibi et al., 2008; Najibi et al., 2015;

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Najibi et al., 2009; Seo et al., 2009; Wang et al., 2008). Hydrates are also interesting for researchers in other areas such as gas separation (Babu et al., 2014; Eslamimanesh et al., 2012a) water desalination (Javanmardi and Moshfeghian, 2003) and air conditioning systems (Wang et al., 2014). However, high formation pressure and low temperature have been a difficulty to their widespread use at industrial scale. To ease the hydrate formation conditions, some materials

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known as “hydrate promoters” are usually added to the aqueous solution to change the hydrate stability conditions to higher temperature or lower pressure and concurrently alter the selectivity

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of the hydrogen-bonded water lattice for entrapping the guest molecules (Douzet et al., 2013; Gholinezhad et al., 2011; Zhong and Englezos, 2012). Several types of promoters have been used

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to change the operating conditions of hydrate formation. One of them is tetra-n-butyl-ammonium bromide (TBAB) which forms semi-clathrate hydrate at lower pressures and can change the hydrogen bonded cages produced by water molecules (Dyadin and Udachin, 1984; Shimada et al., 2005). Investigating the crystals of TBAB hydrates show that the functional group of ionic guest molecules can make a physical bond with water molecules of the lattice and the alkyl chains will be trapped in the large cavities, where dodecahedral cages remain empty (Jeffrey, 1984; Shimada et al., 2005). Several authors have shown that the small gas molecules such as H2, 2

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H2S, CO2, CH4, N2 and O2 selectively can be trapped in available dodecahedral cages (Arjmandi et al., 2007; Mohammadi et al., 2011).

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Prediction the phase stability of the semi-clathrate hydrates is more complex than clathrate hydrates and requires more investigation. There are many reasons for this complexity. Depend on the initial TBAB concentration, this salt can form several structures of semi-clathrate

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hydrates with different stoichiometric compositions (Komatsu et al., 2013). The most wellknown structures are those proposed by Oyama et al. (Oyama et al., 2005) as type A and B with

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stoichiometric compositions of 0.427 and 0.32 mass fraction TBAB respectively. Besides, different hydration numbers are reported for these two types of hydrates (Asaoka et al., 2013); (Kumano et al., 2006; Oyama et al., 2005). It is worth noting that co-existence of two or more hydrate phases is also possible especially at water rich conditions (Sizikov et al., 2012).

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Likewise, as discussed by Lee et al. (Lee et al., 2011), even current advanced experimental techniques, cannot provide accurate information on cage occupancy of semi-clathrate hydrates.

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The experimental data and theoretical models available to explain this phenomenon are limited (Eslamimanesh et al., 2012b; Joshi et al., 2012; Mohammadi et al., 2010; Mohammadi et

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al., 2011; Paricaud, 2011). Main assumption in the available models for prediction of TBAB semi-clathrate hydrate phase equilibrium is "complete dissociation of salt in aqueous solution" while TBAB will partially dissociate in water even at low and moderate concentrations (Buchner et al., 2002; Mbuna et al., 2004). It is of great importance to develop a robust thermodynamic model to overcome this assumption.

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In this work, new experimental data have been measured for hydrate-liquid-vapor (HLW-V) phase equilibrium conditions of CH4+TBAB+H2O system. A thermodynamic model is also developed to predict the phase stability of semi-clathrate hydrates of this system. In the

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developed model, the activity coefficients of components in aqueous phase are calculated using BiMSA electrolyte model and modified Peng-Robinson equation of state (PR-EoS) is applied to

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calculate the gaseous phase fugacity.

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2. Experimental

2.1 Chemicals

Table 1 reports the purities and suppliers of chemicals used in this work. The solutions

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2.2 Apparatus

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are prepared by gravimetric method using a digital balance with the accuracy of ±0.0001 g.

A 100 cm3 autoclave with maximum working pressure of 40 MPa is used to measure all

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the experimental data in this work. A schematic diagram of this setup is shown in Fig. 1. The equilibrium cell is made of stainless steel 316 and is equipped with a 4 blade magnetic stirrer. The temperature in the cell is controlled by circulating coolant through a jacket surrounding the cell. The temperatures are measured using Platinum resistance thermometer sensors (Pt-100) calibrated by Electrical Research and Development Association (ERDA) with an accuracy of 0.1 K. The pressure inside the cell is measured using a pressure transducer (WIKA instrument,

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Model A10) with an accuracy of 0.01 MPa and calibrated by ERDA. The calibration of the pressure transducer is checked regularly using an accurate digital pressure gage (Ashcroft,

acquisition system to be saved on a desktop computer.

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2.3 Experimental procedure

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1070299) with accuracy of 0.001MPa. The measured temperatures and pressure are sent to a data

The measurements made in this work are carried out using a stepwise heating method

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(Tohidi et al., 2000). TBAB salt is added to de-ionized water to prepare the desired solution. At the beginning, 25% (by volume) of the cell is filled with prepared solution and then, the reactor is evacuated to a vacuum level of 10-2 mbar and is purged by methane three times. After that, cell is pressurized with methane gas up to desired pressure level. The temperature of the cell is

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decreased slowly while the mixture is stirred at 400 rpm to ensure hydrate of methane in the presence of TBAB form. The minimum temperature in the cell is carefully determined to be above the pure TBAB semi-clathrate hydrate formation temperature. The cell content

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temperature is then increased slowly with a rate of 0.15 K/h. The semi-clathrate hydrate dissociation point for the studied system is where the slope of the pressure-temperature diagram

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changes suddenly (Najibi et al., 2009; Tohidi et al., 2000). A typical cooling-heating curve measured for 0.15 mass fraction TBAB in aqueous solution is shown in Fig. . Experimental uncertainty in this work is determined using the method given by National Institute of Standards and Technology – NIST (Taylor and Kuyatt, 1994). Results reveal that the maximum combined standard uncertainties, uc, for the temperature and pressure measurements are approximately uc(T)=0.2 K and uc(P)=0.025 MPa, respectively.

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3. Thermodynamic model

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The thermodynamic model proposed in this work is a two steps method. In the first step, the dissociation conditions of pure TBAB semi-clathrate hydrate (H-Lw) are predicted based on Gibbs energy minimization criterion. In the second step, statistical thermodynamic model of van der Waals–Platteeuw (van der Waals and Plateeuw, 1959) is combined with the developed model

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for pure TBAB hydrate to predict the phase stability conditions of TBAB + methane semi-

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clathrate hydrate.

3.1 H-Lw phase equilibrium

Semi-clathrate hydrate of pure TBAB in water at a given temperature and pressure can be

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described by Gibbs energy minimization method as explained by Paricaud (Paricaud, 2011). The overall equation that describes this phase equilibrium is as follows:

RT ∆V

0

( P0 )

RT

RT

∆h 0 (T 0 , P0 )  1 1  ∆c p0 (T 0 )  T 0  ∆c p0 (T 0 )  T 0  + ln    − −  T − 1 + R R R   T  T T 0  (1)

( P − P0 ) + ln ( K ovP ) = 0 0

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+

=

∆g 0 (T 0 , P0 )

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∆g dis (T , P )

In this equation, ∆c p0 is the molar heat capacity difference which is set to zero to reduce

the adjustable parameters and the detail description of other parameters are described by Paricaud (Paricaud, 2011). In this equation K ovP0 is the overall reaction constant for pure TBAB semi-clathrate hydrate formation at P0. The attempt in this work is to find a suitable procedure to calculate this overall equilibrium constant at P0, as described below.

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Pure TBAB forms a stoichiometric semi-clathrate hydrate crystal which contains νW water molecules per molecule of salt in aqueous solution. The equilibrium reaction for

K1 C v C Av A .v W H 2O ( H ) ←→ v C C z C ( aq ) + v A A

z

A

( aq ) + v W H 2O ( L W )

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dissociation of this hydrate is as follows: (2)

Furthermore, the association reaction between the ionic compounds present in the aqueous solution at constant temperature can be written as follows: z

A

K ( aq ) ←→ [C .A ]ip ( aq )

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C z C ( aq ) + A

2

(3)

K ov CA .v W H 2O ( H ) ← → αC z C ( aq ) + α A

z

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Combining Eqs. (2) and (3) leads to the following equation: A

( aq ) + (1 − α ) [C .A ]ip ( aq ) + v W H 2O ( L )

(4)

From basic reaction kinetic, the overall equilibrium constant (Kov) for this reaction can be calculated as follows: (1−α )

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K ov = K 1. ( K 2 )

(5)

In this equation α is unbound ion fraction and K1 is expressed in terms of composition as bellow: W

) exp  −

1   RT

P0

∫ (v

W

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( aC )( a A ) ( aWv K1 = ( aH )

P

 VW0 + vCVC∞ + v AVA∞ − VH0 dP   

)

(6)

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At P0, the exponential term vanishes, aH which is the activity of pure salt hydrate is accounted unity and K2 and α are determined using electrolyte model. Finally the term K ovP0 defined in Eq. (1) reduces to the following equation at molarity scale assuming that hydration of ions in solution is negligible.

K ovP0 = [αC S y ± ] aWvW K 2( v

1−α )

(7)

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3.2 Electrolyte model

In this work, BiMSA model proposed by Bernard and Blum (Bernard and Blum, 1996) is

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used to find the activities of species in the liquid phase. This model can predict the properties of non-ideal salt solutions up to high concentrations and its detail description is presented elsewhere (Bernard and Blum, 1996; Papaiconomou et al., 2012; Simonin et al., 1998). The two parameters

function of salt concentration and temperature as follows:

(

)

ε −1 = εW−1 (1 + βC S + βT C S (T − 298.15 ) )

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σ C = σ C( 0 ) + σ C(1)C S + σ C( 0.T) + σ C(1,)T CS (T − 298.15 )

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of this model, σ C (diameter of cation) and ε (the relative permittivity) are described as a

(8) (9)

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σ C( 0 ) , σ C(1) and β are fitted using the experimental data reported in the literature for the mean ionic activity coefficients and osmotic coefficients of electrolyte solutions at 298.15 K and P=0.10 MPa (Hamer and Wu, 1972; Lindenbaum and Boyd, 1964). Other parameters including

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1 σ C( 0.T) , σ C( ,)T and βT are fitted using the experimental data reported in the literatures for relative

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apparent molal enthalpy ( Lφ ) (Mayrath and Wood, 1983; Parker, 1965). Lφ for these salts can be determined from the following relation (Simonin et al., 2008):

Lφ = ν RT

∂ (φ − ln γ ± )

(10)

∂T

The optimized values of these parameters are reported in Tables 2 and 3 which are close to the values reported in the literature. For example, the diameter of the TBAB cation ( σ C( ) ) obtained 0

(8.292 Å) is close to the value of 8.26 Å reported by Marcus (Marcus, 2008). In addition, value 8

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obtained for the association constant (K2) for TBAB solution (2.722 L mol-1) is in fair agreement with the experimental value of 2.51 L mol-1 reported in (Mbuna et al., 2004).

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It is worth noting that, all of the parameters appeared in Eq. (1) has a relation with electrolyte model in somehow (Kwaterski and Herri, 2011a; Paricaud, 2011). Therefore improving the electrolyte model used, will increase the accuracy of final results. In the

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electrolyte model developed in this work, the association of ions (ion paring) is considered and this has improved the predictions of ionic model. To show this improvement, the accuracies of

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the electrolyte model developed in this work and the SAFT-VRE model used by Paricad (Paricaud, 2011) for the predictions of activity, osmotic coefficients and apparent molal enthalpies of LiBr and TBAB are compared in Table 4. The association of ions is not considered by Paricad and the results reported in Table 4 show that considering this effect will improve the

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predictions of electrolyte model.

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3.3 H-Lw-V phase equilibrium

According to the vdW-P statistical thermodynamic model, conventionally, the

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hypothetical empty hydrate is selected as the reference state for calculation of the chemical potential of water in the hydrate phase. As described by Papadimitriou et al. (Papadimitriou et al., 2009), in the semi-clathrate hydrate of promoters such as TBAB, empty hydrate reference state can be replaced by the cavity filled with pure promoter. Therefore, the hydrate stability conditions of methane + TBAB + water system can be predicted by the following equation:

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∆g dis (T , P ) RT ∆v 0 ( P0 ) RT

=

∆g 0 (T 0 , P0 ) RT

∆h 0 (T 0 , P0 )  1 1  ∆c p0 (T 0 )  T 0  ∆c p0 (T 0 )  T 0  ln   + +  − −  T − 1 + R R R   T  T T0  (11)

( P − P0 ) + ln ( K ovP ) + n small ln (1 + C smallf g ) = 0 0

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where nsmall is the number of small cavities per salt molecule in unit hydrate cell, fg is the fugacity of the gaseous hydrate former which is calculated by the modified Peng Robinson equation of state (PR-EoS) (Melhem et al., 1989) and Csmall is the Langmuir adsorption constant

aa  bb  exp   T T 

(12)

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C small =

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and is calculated with the method proposed by Parrish and Prausnitz (1972) as bellow:

The two adjustable parameters in this equation (aa and bb) are optimized using some literature data (Arjmandi et al., 2007; Gholinezhad et al., 2011; Lee et al., 2011; Mohammadi et al., 2011; Mohammadi and Richon, 2009; Sangwai and Oellrich, 2014; Sun and Sun, 2010). Genetic

Table 5.

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algorithm method is used to optimize these parameters and the optimized values are reported in

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4. Results and discussion

4.1 Aqueous solution properties

To check the validity of electrolyte model developed in the present work, the

thermodynamic properties of some aqueous electrolyte solutions, including LiBr, LiOH, HNO3 and TBAB are predicted using this model. LiBr from alkali halides group is a non-ideal system with a high associative behavior. HNO3 shows strong acidic effects up to high concentrations 10

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and LiOH is the weakest base among the alkali metal hydroxides. The predicted values for activity coefficients and osmotic coefficients of these solutions are compared with the experimental data in Figs. 3a and 3b respectively. Moreover, predicted degrees of association of

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HNO3 are also compared with the experimental data in Fig. 4 for concentrations up to 11 mol L-1. The results shown in these figures clearly illustrate that the electrolyte model developed in this work has a very good accuracy for aqueous phase properties predictions for very different

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4.2 H-Lw phase equilibrium

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solutions.

Pure TBAB in water forms semi-clathrate hydrate at the appropriate temperature and pressure with different structures. Stability of each structure depends on the concentration of

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TBAB in solution. As reported by Oyama et al. (Oyama et al., 2005), for salt concentrations less than 18 wt.%, type B is more stable.

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All the parameters required to solve Eq. (1) are optimized by genetic algorithm (GA) global optimization method using available experimental data and the results are reported in

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Table 6. The optimized values for these parameters are in very good agreement with the values reported by Oyama et al. (Oyama et al., 2005). Hydrate formation conditions of pure TBAB for different salt concentrations predicted by the developed model in this work, are shown in Fig. 5. Moreover, the experimental data reported by Arjmandi et al, (Arjmandi et al., 2007) for 0.10 mass fraction TBAB are also shown in this figure. As shown, the developed model predicts the experimental data very good.

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The experimental data found in literature for melting temperature of pure TBAB semiclathrate hydrates in atmospheric pressure for different salt concentrations are shown in Fig. 6. The predictions of developed model in this work for structures A and B are also shown in this

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figure. Left hand side curve is the model predictions for type B and right hand side curve is for type A. The two curves intersect at TBAB mass fraction of 0.172 very close to the experimental value of 0.18 reported in the literature (Oyama et al., 2005; Sakamoto et al., 2008). As discussed

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by Oyama et al. (Oyama et al., 2005), congruent melting point composition for each type of pure TBAB hydrate is the composition in which the highest melting temperature happens. Fig. 6

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shows that the congruent melting point compositions for types A and B are predicted to be 0.42 and 0.325 mass fractions respectively, near to the experimental values of 0.40 and 0.32 mass fractions reported by Oyama (Oyama et al., 2005). This figure shows that the developed model is

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able to predict the rheological behavior of different types of TBAB hydrate satisfactorily.

4.3 H-Lw-V phase equilibrium

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The three phase (H-LW-V) stability conditions of the CH4+TBAB+H2O system have been

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measured for 0.05, 0.15 and 0.30 mass fractions of TBAB in this work. Experiments are carried out for the pressure range of 2.88 – 14.1 MPa and temperature range of 285.6 – 295.9 K and the results are reported in Table 7. The measured values are compared with the experimental data obtained from open literatures for different TBAB concentrations and pure water in Fig. 7. The results show that addition of TBAB into water promotes hydrate formation and shifts the hydrate stability region to the right. It also shows that there is a good agreement between the data measured in this work and the data reported in the literature. 12

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The predictions of the model developed in this work for semi-clathrate hydrate formation conditions of methane with TBAB are compared with the experimental data collected from literature and measured in this work in Fig. 8. Results show that the model developed in this

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work can predict the phase stability conditions of TBAB + methane semi-clathrate hydrate with good accuracy. As shown in this figure, addition of TBAB into water up to near 0.40 mass fraction, shifts the hydrate stability zone to the right (promotion effect). By increasing the mass

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fraction of TBAB from 0.4, the hydrate stability zone begins to shift to the left (inhibition effect). The predictions of the developed model also shows these trends showing that this model has the

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capability of prediction the promotion and inhibition effects of TBAB. The average absolute relative deviation between the predictions of the model and reported data is 12%.

To demonstrate the effect of chosen electrolyte model on the final predictions of H-LW-V

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phase equilibrium of CH4+TBAB+H2O system, BiMSA electrolyte model have been changed with Non-Random Two Liquid (e-NRTL) model (Chen and Evans, 1986, Kwaterski and Herri 2011b). e-NRTL model do not consider the association effects of ions and its parameters are

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found from Belvèze et al. (Belvèze et al., 2004). The parameters required to solve equation (1) for the new model are optimized with the same procedure as discussed in previous sections and

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the results are reported in Tables 5 and 6.

The final predictions of the thermodynamic models for H-LW-V phase equilibrium of

CH4+TBAB+H2O system in the two cases of e-NRTL and BiMSA as electrolyte models, are compared with the experimental data in Fig. 9. The results show that the thermodynamic model which uses BiSMA for the aqueous phase, predicts experimental data much better. This can lead

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to this conclusion that considering the association effect in the electrolyte model, can improve the predictions of the developed thermodynamic model for hydrate phase equilibrium of methane

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with TBAB aqueous solution.

5. Conclusions

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New experimental data for the phase stability conditions of TBAB + methane semiclathrate hydrate in a wide range of temperature, pressure and salt concentration are measured. A

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thermodynamic model is also proposed to estimate the dissociation conditions of semi clathrate hydrates for this system. In the proposed model, modified binding mean spherical approximation electrolyte model (BiMSA) with considering the association effects of ions is used for aqueous phase properties prediction and the gaseous phase fugacity is calculated by the modified Peng

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Robinson equation of state. The activity coefficient, osmotic coefficient, association constant and molal enthalpy for some electrolyte solutions are predicted using this model. The results show that the predicted values are in good agreement with the literature data. The developed

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thermodynamic model for the phase stability conditions of TBAB + methane semi-clathrate hydrate, predicts the experimental data satisfactorily with Average Absolute Relative Deviation

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of 12%. Moreover, the model is able to predict the different types of pure TBAB semi-clathrate hydrates and also the inhibition and promotion effects of this salt. The results also show that considering the association effect in the electrolyte model, can improve the predictions of the developed thermodynamic model for hydrate phase equilibrium of methane in the presence of TBAB aqueous solution.

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Nomenclature

temperature

P

pressure

N

number of data

C

cation

A

anion

g

molar Gibbs free energy

h

molar enthalpy

cP

molar heat capacity

V

molar volume

R

universal gas constant

K

equilibrium constant

[C .A ]ip

ion-pair assuming as neutral species

ai

activity of species ion (i: C, A)

CS

molarity of salt

aW

activity of water

n small

number of small cages per salt molecule

C small

Langmuir adsorption constant for small cages

Lφ aa

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f

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T

bb

fugacity of the gaseous hydrate former molal enthalpy parameter of Langmuir adsorption constant parameter of Langmuir adsorption constant

Greek letters

σ

diameter 15

relative permittivity

y±

mean ionic activity coefficient in the molarity scale

φ

osmotic coefficient

γ±

mean ionic activity coefficient in the molality scale

β

concentration dependent parameter of permitivity

v

stoichiometric number (v= vC+ vA)

α

unbound ion fraction

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ε

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Superscripts/ Subscripts water

S

salt

C

cation

A

anion

dis

dissociation

0

standard conditions

∞

infinite dilution

g

gas

ov

overall

Z

ion charge

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W

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References Arjmandi, M., Chapoy, A., Tohidi, B., 2007. Equilibrium Data of Hydrogen, Methane, Nitrogen, Carbon Dioxide, and Natural Gas in Semi-Clathrate Hydrates of Tetrabutyl Ammonium

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Bromide. J. Chem. Eng. Data 52, 2153-2158.

Asaoka, T., Kumano, H., Serita, M., 2013. Measurement of latent heat of tetra-nbutylammonium bromide (TBAB) hydrate. Int. J. Refrig. 36, 992-997.

Babu, P., Chin, W.I., Kumar, R., Linga, P., 2014. Systematic Evaluation of Tetra-n-butyl

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Ammonium Bromide (TBAB) for Carbon Dioxide Capture Employing the Clathrate Process. Ind. Eng. Chem. Res. 53, 4878-4887.

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Belvèze, L.S., Brennecke, J.F., Stadtherr, M.A., 2004. Modeling of Activity Coefficients of Aqueous Solutions of Quaternary Ammonium Salts with the Electrolyte-NRTL Equation. Ind. Eng. Chem. Res. 43, 815-825.

Bernard, O., Blum, L., 1996. Binding mean spherical approximation for pairing ions: An exponential approximation and thermodynamics. J. Chem. Phys. 104, 4746-4754. Buchner, R., Holzl, C., Stauber, J., Barthel, J., 2002. Dielectric spectroscopy of ion-pairing and

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hydration in aqueous tetra-n-alkylammonium halide solutions. Phys. Chem. Chem. Phys. 4, 2169-2179.

Chen, C.-C., Evans, L.B., 1986. A local composition model for the excess Gibbs energy of aqueous electrolyte systems. AIChE 32, 444-454.

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Douzet, J., Kwaterski, M., Lallemand, A., Chauvy, F., Flick, D., Herri, J.-M., 2013. Prototyping of a real size air-conditioning system using a tetra-n-butylammonium bromide semiclathrate

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hydrate slurry as secondary two-phase refrigerant – Experimental investigations and modelling. Int. J. Refrig. 36, 1616-1631. Dyadin, Y.A., Udachin, K.A., 1984. Clathrate formation in water-peralkylonium salts systems. J. inclu. phenom. 2, 61-72.

Eslamimanesh, A., Mohammadi, A.H., Richon, D., 2012b. Thermodynamic modeling of phase equilibria of semi-clathrate hydrates of CO2, CH4, or N2+tetra-n-butylammonium bromide aqueous solution. Chem. Eng. Sci. 81, 319-328.

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Eslamimanesh, A., Mohammadi, A.H., Richon, D., Naidoo, P., Ramjugernath, D., 2012a. Application of gas hydrate formation in separation processes: A review of experimental studies. J. Chem. Thermodyn. 46, 62-71. Gholinezhad, J., Chapoy, A., Tohidi, B., 2011. Thermodynamic stability and self-preservation

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properties of semi-clathrates in the methane+tetra-n-butyl ammonium bromide+water system, Int. Conference on Gas Hydrates (ICGH), Edinburgh, Scotland, United Kingdom.

Gudmundsson, J.S., 1996. Method for production of gas hydrates for transportation and storage. Google Patents.

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Hamer, W.J., Wu, Y.C., 1972. Osmotic Coefficients and Mean Activity Coefficients of Uniunivalent Electrolytes in Water at 25°C. J. Phys. Chem. Ref. Data 1, 1047-1100.

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Javanmardi, J., Moshfeghian, M., 2003. Energy consumption and economic evaluation of water desalination by hydrate phenomenon. App. Therm. Eng. 23, 845-857. Jeffrey, G.A., 1984. Hydrate inclusion compounds. J. incl. phenom. 1, 211-222. Joshi, A., Mekala, P., Sangwai, J.S., 2012. Modeling phase equilibria of semiclathrate hydrates of CH4, CO2 and N2 in aqueous solution of tetra-n-butyl ammonium bromide. J. Natural Gas Chem. 21, 459-465.

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Komatsu, H., Hayasaka, A., Ota, M., Sato, Y., Watanabe, M., Smith Jr, R.L., 2013. Measurement of pure hydrogen and pure carbon dioxide adsorption equilibria for THF clathrate hydrate and tetra-n-butyl ammonium bromide semi-clathrate hydrate. Fluid Phase Equilib. 357, 80-85. Kumano, H., Saito, A., Okawa, S., Goto, Y., 2006. Study on Fundamental Characteristics of

EP

TBAB Hydrate Slurry. Trans. Jpn. Soc. Mech. Eng. B 72, 3089-3095. Kwaterski, M., Herri, J.M., 2011a. Thermodynamic modelling of gas semi-clathrate hydrates

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using the electrolyte NRTL model, Int. Conference on Gas Hydrates (ICGH), Edinburgh, Scotland, United Kingdom.

Kwaterski, M., Herri, J.M., 2011b. Modelling Gas Hydrate equilibria Using The electrolyte NonRandom Two-Liquid (eNRTL) model. Int. Conference on Gas Hydrates (ICGH) Edinburgh, Scotland, United Kingdom.

Lee, S., Park, S., Lee, Y., Lee, J., Lee, H., Seo, Y., 2011. Guest Gas Enclathration in Semiclathrates of Tetra-n-butylammonium Bromide: Stability Condition and Spectroscopic Analysis. Langmuir 27, 10597-10603.

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Lindenbaum, S., Boyd, G.E., 1964. Osmotic and Activity Coefficients for the Symmetrical Tetraalkyl Ammonium Halides in Aqueous Solution at 25°C. J. Phys. Chem. 68, 911-917. Mayrath, J.E., Wood, R.H., 1983. Enthalpies of dilution of aqueous solutions of two hydrophobic solutes: t-butanol and tetra-n-butylammonium bromide, at 348.15 to 423.65 K. J. Chem.

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Thermodyn. 15, 625-632.

Mbuna, J., Takayanagi, T., Oshima, M., Motomizu, S., 2004. Evaluation of weak ion association between tetraalkylammonium ions and inorganic anions in aqueous solutions by capillary zone electrophoresis. J. Chroma. A 1022, 191-200.

SC

Melhem, G.A., Saini, R., Goodwin, B.M., 1989. A modified Peng-Robinson equation of state. Fluid Phase Equilib. 47, 189-237.

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Mohammadi, A.H., Belandria, V., Richon, D., 2010. Use of an artificial neural network algorithm to predict hydrate dissociation conditions for hydrogen+water and hydrogen+tetra-nbutyl ammonium bromide+water systems. Chem. Eng. Sci. 65, 4302-4305. Mohammadi, A.H., Eslamimanesh, A., Belandria, V., Richon, D., 2011. Phase Equilibria of Semiclathrate Hydrates of CO2, N2, CH4, or H2 + Tetra-n-butylammonium Bromide Aqueous Solution. J. Chem. Eng. Data 56, 3855-3865.

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Mohammadi, A.H., Richon, D., 2009. Phase Equilibria of Semi-Clathrate Hydrates of Tetra-nbutylammonium Bromide + Hydrogen Sulfide and Tetra-n-butylammonium Bromide + Methane. J. Chem. Eng. Data 55, 982-984.

Najibi, H., Chapoy, A., Tohidi, B., 2008. Methane/natural gas storage and delivered capacity for

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activated carbons in dry and wet conditions. Fuel 87, 7-13. Najibi, H., Mirzaee Shayegan, M., Heidary, H., 2015. Experimental investigation of methane

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hydrate formation in the presence of copper oxide nanoparticles and SDS. J. Natural Gas Sci. Eng. 23, 315-323.

Najibi, H., Mohammadi, A.H., Tohidi, B., 2006. Estimating the Hydrate Safety Margin in the Presence of Salt and/or Organic Inhibitor Using Freezing Point Depression Data of Aqueous Solutions. Ind. Eng. Chem. Res. 45, 4441-4446. Najibi, H., Rezaei, R., Javanmardi, J., Nasrifar, K., Moshfeghian, M., 2009. Economic evaluation of natural gas transportation from Iran’s South-Pars gas field to market. App. Therm. Eng. 29, 2009-2015.

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Oyama, H., Shimada, W., Ebinuma, T., Kamata, Y., Takeya, S., Uchida, T., Nagao, J., Narita, H., 2005. Phase diagram, latent heat, and specific heat of TBAB semiclathrate hydrate crystals. Fluid Phase Equilib. 234, 131-135. Papadimitriou, N.I., Tsimpanogiannis, I.N., Stubos, A.K., 2009. Gas content of binary clathrate

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hydrates with promoters. J. Chem. Phys. 131, 044102-044101-044110.

Papaiconomou, N., Simonin, J.-P., Bernard, O., 2012. Solutions of Alkylammonium and Bulky Anions: Description of Osmotic Coefficients within the Binding Mean Spherical Approximation. Ind. Eng. Chem. Res. 51, 9661-9668.

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Paricaud, P., 2011. Modeling the Dissociation Conditions of Salt Hydrates and Gas Semiclathrate Hydrates: Application to Lithium Bromide, Hydrogen Iodide, and Tetra-n-

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butylammonium Bromide + Carbon Dioxide Systems. J. Phys. Chem. B 115, 288-299. Parker, V.B., 1965. Thermal Properties of Aqueous Uni-Unilvalent Electrolytes, National Standard Reference Data Series (NSRDS).

Parrish, W.R., Prausnitz, J.M., 1972. Dissociation Pressures of Gas Hydrates Formed by Gas Mixtures. Ind. Eng. Chem. Proc. Des. Dev. 11, 26-35.

Sakamoto, J., Hashimoto, S., Tsuda, T., Sugahara, T., Inoue, Y., Ohgaki, K., 2008.

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Thermodynamic and Raman spectroscopic studies on hydrogen+tetra-n-butyl ammonium fluoride semi-clathrate hydrates. Chem. Eng. Sci. 63, 5789-5794. Sangwai, J.S., Oellrich, L., 2014. Phase equilibrium of semiclathrate hydrates of methane in aqueous solutions of tetra-n-butyl ammonium bromide (TBAB) and TBAB–NaCl. Fluid Phase

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Equilib. 367, 95-102.

Seo, Y., Lee, J.W., Kumar, R., Moudrakovski, I.L., Lee, H., Ripmeester, J.A., 2009. Tuning the

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composition of guest molecules in clathrate hydrates: NMR identification and its significance to gas storage. Chem. Asian J. 4, 1266-1274. Shimada, W., Shiro, M., Kondo, H., Takeya, S., Oyama, H., Ebinuma, T., Narita, H., 2005. Tetra-n-butylammonium bromide-water (1/38). Acta Crystallogr. Sect. C: Cryst. Struct. Commun. 61, o65-o66.

Simonin, J.-P., Bernard, O., Blum, L., 1998. Real Ionic Solutions in the Mean Spherical Approximation. 3. Osmotic and Activity Coefficients for Associating Electrolytes in the Primitive Model. J. Phys. Chem. B 102, 4411-4417.

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Simonin, J.-P., Bernard, O., Papaiconomou, N., Kunz, W., 2008. Description of dilution enthalpies and heat capacities for aqueous solutions within the MSA–NRTL model with ion solvation. Fluid Phase Equilib. 264, 211-219. Sizikov, A.A., Manakov, A.Y., Rodionova, T.V., 2012. Methane Capacity of Double

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Tetrabutylammonium Bromide + Methane Ionic Clathrate Hydrates. Energy & Fuels 26, 37113716.

Sloan, E.D., Koh, C.A., 2008. Clathrate Hydrates of Natural Gases. CRC Press, Taylor & Francis Group, Boca Raton.

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Sun, Z.-G., Sun, L., 2010. Equilibrium Conditions of Semi-Clathrate Hydrate Dissociation for Methane + Tetra-n-butyl Ammonium Bromide. J. Chem. Eng. Data 55, 3538-3541.

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Taylor, B.N., Kuyatt, C.E., 1994. Guidlines for Evaluating and Expressing the Uncertainty of NIST Measurement Results. Adapted from NIST Technical Note 1297. Tohidi, B., Burgass, R.W., Danesh, A., ØStergaard, K.K., Todd, A.C., 2000. Improving the Accuracy of Gas Hydrate Dissociation Point Measurements. Ann. N.Y. Acad. Sci. 912, 924-931. van der Waals, J.H., Plateeuw, C., 1959. Clathrate Solutions. Adv. Chem. Phys. 2, 1-57. Wang, W., Bray, C.L., Adams, D.J., Cooper, A.I., 2008. Methane Storage in Dry Water Gas

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Hydrates. J. Am. Chem. Soc. 130, 11608-11609.

Wang, X., Dennis, M., Hou, L., 2014. Clathrate hydrate technology for cold storage in air conditioning systems. Ren. Sustain. Energy Rev. 36, 34-51. Zhong, D., Englezos, P., 2012. Methane Separation from Coal Mine Methane Gas by Tetra-n-

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butyl Ammonium Bromide Semiclathrate Hydrate Formation. Energy Fuels 26, 2098-2106.

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Figures captions:

-

Schematic of the experimental set-up: (1) the equilibrium cell; (2) cooling bath

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Fig. 1

circulator; (3) gas cylinder; (4) pressure transducer; (5) temperature transducer; (6) stirrer; (7) PC; (8) motor.

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Fig. 2 - Cooling-heating curve measured for 0.15 mass fraction TBAB in aqueous solution.

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Fig. 3 – Developed model predictions and experimental data for (a) mean activity coefficients and (b) osmotic coefficients for aqueous solutions of LiOH, LiBr, HNO3 and TBAB at 298.15 K.

Fig. 4 – Model predictions and experimental data for associated nitric acid molarity in aqueous solutions versus initial concentration at 298.15 K.

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Fig. 5 – Model predictions and experimental data for phase diagram of pure TBAB semiclathrate hydrates at different TBAB concentrations.

Fig. 6 – Model predictions and experimental data for melting temperature of pure TBAB semi-

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clathrate hydrate versus salt concentration.

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Fig. 7 – Phase diagram of methane hydrate with TBAB in aqueous solution (experimental data). Fig. 8 - Phase diagram of methane hydrate with TBAB in aqueous solution (experimental data + model predictions).

Fig. 9 – Comparison of the predictions of two thermodynamic models for methane hydrate with TBAB in aqueous solution with experimental data.

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Methane

Persian Gas

TBAB

Merck a

Purity (mole fraction) 0.99995

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Supplier

≥0.99

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Chemical

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Table 1: Purities and suppliers of chemicals a

Deionized water is used in all experiments

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Table 2. Optimized values of parameters for the developed electrolyte model at T=298.15 K and P=0.1MPa.

Comp.

σ C( ) (Å)

Max m

0

LiBr

4

5.685

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LiOH

1

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(mol kg-1)

σ C( ) (Å L mol-1)

K2 β %AARDΦa %AARDγ±b -1 -1 (L mol ) (L mol )

-0.129

0.109

1.531

0.279

0.095

20

5.686

-0.107

0.126

0.252

0.618

1.654

HNO3

28

4.780

-0.069

0.062

0.080

1.118

2.067

TBAB

10

8.292

-0.364

0.677

2.722

4.163

2.429

a

AARDφ = (100 N

) ∑ j =1 φcal ( j ) − φexp ( j ) N

φexp ( j ) , b AARD γ = (100 N ) ∑ j =1 γ ± ,cal ( j ) − γ ± ,exp ( j ) γ ± ,exp ( j ) , N

±

where N is the number of experimental data points.

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Table 3. Optimized values of temperature dependent parameters for the developed electrolyte

( 0) ×10-3 σ C.T (Å K-1)

( 1) σ C,T ×10-4 (Å L mol-1 K-1)

(L mol K )

LiOH

0

1.781

3.418

LiBr

1.050

0.291

HNO3

5.560

TBAB

5.297

%AARDLφa

-1

2.305

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-1

0

0

1.189

18.310

2.860

102.64

27.016

) ∑ j =1 Lφ ,cal ( j ) − Lφ ,exp ( j ) N

10.810

Lφ ,exp ( j ) , where N is the number of experimental data points.

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AARD Lφ = (100 N

βT ×10-4

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Comp.

a

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model.

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Table 4. %AARDa for the predictions of developed electrolyte model and SAFT-VREb equation of state.

Φ

LΦ

Our model SAFT-VRE

Our model SAFT-VRE

Our model SAFT-VRE

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γ±

Comp.

LiBr

1.654

6.9

0.618

2.5

10.810

7.7

TBAB

3.429

3.9

4.163

4.6

27.016

26

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a

AARD X = (100 N

) ∑ j =1 X cal ( j ) − X exp ( j ) N

X exp ( j ) , where N is the number of experimental data points and

X cab be γ±, Φ or LΦ.

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ref. (Paricaud, 2011)

Table 5. Langmuir adsorption constant parameters for small cavities, Csmall , Eq. (12). Type B

35.082

e-NRTL

0.011

aa×10-4 (K MPa-1)

bb (K)

2959.0

1.141

3975.6

0.186

4521.0

6590.0

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BiMSA

bb (K)

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Liq. model aa×10-4 (K MPa-1)

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Type A

Table 6. Values of parameters used for solving Eq. (1).

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BiMSA

Type

A B

vW

ni

e-NRTL

∆h 0

∆V 0

T0

∆h 0

∆V 0

(K)

(kJ mol-1)

(cm3 mol-1)

(K)

(kJ mol-1)

(cm3 mol-1)

T0

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b

26

2

284.85

149.90

-26.53

285.15

152.76

-18.87

38

3

283.50

199.90

-26.53

283.03

200.98

-18.87

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Temperature (K) Pressure (MPa) 2.88

287.2

4.98

290.4

9.85

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285.6

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Table 7. Measured values of CH4 Semi-clathrate hydrate stability conditions at different mass fractions of TBAB in aqueous solution 0.05 Mass Fraction of TBAB

291.0

12.5

0.15 Mass Fraction of TBAB

Temperature (K) Pressure (MPa) 3.33

291.4

5.11

293.3

8.49

295.1

13.1

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289.3

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0.30 Mass Fraction of TBAB

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Temperature (K) Pressure (MPa) 290.0

3.05

291.7

5.13

294.5

8.42

295.9

14.1

a

Standard uncertainty, uc, in TBAB mass fraction, hydrate dissociation temperature, and hydrate dissociation pressure, are uc(mass fraction) = 0.001, uc(T) = 0.2 K, uc(P) = 0.025 MPa, respectively.

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Fig 1.

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Fig 2.

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Fig 3.

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Fig 3.

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Fig 4.

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Fig 5.

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Fig 6.

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Fig 7.

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Fig 8.

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WTBAB = 0.2 Arjmandi et al., 2007; Sun and Sun, 2010; Sangwai and Oellrich, 2014

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W TBAB = 0.45 Sun and Sun, 2010

Model predictions for WTBAB = 0.2 with BiMSA for liquid phase Model predictions for W

TBAB

= 0.2 with e-NRTL for liquid phase

Model predictions for WTBAB = 0.45 with e-NRTL for liquid phase

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Model predictions for WTBAB = 0.45 with BiMSA for liquid phase

Fig. 9

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Research highlight

Hydrate phase equilibrium data are reported for the CH4 + TBAB aqueous solutions systems.

•

A thermodynamic model is developed to predict the dissociation conditions of the latter systems.

•

The properties of the aqueous phase are calculated using modified BiMSA electrolyte model.

•

The model satisfactorily predicts the experimental data with an AARD% of approximately 12%.

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•