Modeling phase equilibria of semiclathrate hydrates of CH4, CO2 and N2 in aqueous solution of tetra-n-butyl ammonium bromide

Journal of Natural Gas Chemistry 21(2012)459–465

Modeling phase equilibria of semiclathrate hydrates of CH4, CO2 and N2 in aqueous solution of tetra-n-butyl ammonium bromide Abhishek Joshi, Prathyusha Mekala,

Jitendra S. Sangwai∗

Petroleum Engineering Program, Department of Ocean Engineering, Indian Institute of Technology Madras, Chennai-600 036, India [ Manuscript received December 23, 2011; revised February 29, 2012 ]

Abstract Semiclathrate hydrates of tetra-n-butyl ammonium bromide (TBAB) offer potential solution for gas storage, transportation, separation of flue gases and CO2 sequestration. Models for phase equilibria for these systems have not yet been developed in open literatures and thus require urgent attention. In this work, the first attempt has been made to model phase equilibria of semiclathrate hydrates of CH4 , CO2 and N2 in aqueous solution of TBAB. A thermodynamic model for gas hydrate system as proposed by Chen and Guo has been extended for semiclathrate hydrates of gases in aqueous solution of TBAB. A correlation for the activity of water relating to the system temperature, concentration of TBAB in the system and the nature of guest gas molecule has been proposed. The model results have been validated against available experimental data on phase equilibria of semiclathrate hydrate systems of aqueous TBAB with different gases as guest molecule. The extended Chen and Guo’s model is found to be suitable to explain the promotion effect of TBAB for the studied gaseous system such as, methane, carbon dioxide and nitrogen as a guest molecule. Additionally, a correlation for the increase in equilibrium formation temperature (hydrate promotion temperature, ΔTp ) of semiclathrate hydrate system with respect to pure gas hydrate system has been developed and applied to semiclathrate hydrate of TBAB with several gases as guest molecules. The developed correlation is found to predict the promotion effect satisfactorily for the system studied. Key words gas hydrate; phase equilibria; semiclathrate hydrate; tetra-n-butyl ammonium bromide (TBAB)

1. Introduction

Gas hydrates, generally referred to as clathrate compounds, are of snowy ice-like structures which are formed when ‘guest’ molecules of gases such as, methane, carbon dioxide, etc., are entrapped in the cages formed by the ‘host’ water molecules. The formation of gas hydrate is expected under high pressure and low temperature conditions. Gas hydrates are found to exhibit many structures like sI, sII and sH depending on the size of the guest molecules [1]. Semiclathrates compounds are formed in the presence of tetra-nalkyl ammonium halides (bromide, TBAB; chloride, TBAC; or fluoride, TBAF) in the system and are not exactly similar to gas hydrates structures but share many of the physical and structural properties as true clathrate hydrates. These were first observed by Fowler et al. [2]. In semiclathrate hydrate compounds, the cages are formed by the halide ions by forming H-bond together with water molecules and the tetra-nalkyl cation occupies four cages, the remaining been occupied

by the guest gas molecules such as, methane, carbon dioxide, etc. [3,4]. Like gas hydrates, semiclathrate hydrates are also capable of selectively trapping large volumes of gases within a molecular framework of water molecules, however, semiclathrate can be formed at a substantially lower pressure than gas hydrates [5]. Semiclathrates have gained attentions due to their potential use, mainly in the storage and transportation of natural gases, separation of gases from industrial exhaust and carbon dioxide sequestration under conditions of low operating pressure and temperature [6−10]. Several researchers [7,11−14] conducted experiments to get the equilibrium formation pressure and temperature conditions for semiclathrate hydrates of methane, nitrogen, carbon dioxide, hydrogen and natural gases with varying weight fractions of TBAB. Meysel et al. [5] performed experiments to determine the equilibrium conditions of formation of semiclathrate hydrates from quaternary mixtures of (CO2 +N2 +TBAB+H2 O). It was observed that the formation pressure required for semiclathrate hydrate at a given temperature for the gases studied decreased significantly with increase

∗

Corresponding author. Tel: +91-44-2257-4825; Fax: +91-44-2257-4802; E-mail: [email protected] This work was supported by the the Industrial Consultancy and Sponsored Research (ICSR), Indian Institute of Technology Madras, Chennai (Project Number OEC/10−11/530/NFSC/JITE) and the National Institute of Ocean Technology (NIOT), Chennai, India (Project Number OEC/10-11/105/NIOT/JITE). Copyright©2012, Dalian Institute of Chemical Physics, Chinese Academy of Sciences. All rights reserved. doi:10.1016/S1003-9953(11)60391-5

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in TBAB concentration. Li et al. [15] and Ding et al. [16] conducted experiments and studied the formation and dissociative behavior of methane gas hydrates in the presence of TBAB. Li et al. [17] studied CO2 capture mechanism using semiclathrate hydrate system of TBAB. They observed that the induction time for hydrate formation using TBAB is quite short (about 5 min), and thus, is a potential tool for CO2 capture. Zhong et al. [18] carried out experiments to predict the formation temperature and pressure conditions for semiclathrate hydrate formed by a mixture of gases in aqueous solution of TBAB. Lang et al. [19] provided a review on the prospects of using clathrate compounds for methane and hydrogen storage application. They stated that the tetra-n-butyl ammonium halide semiclathrate hydrates can be of promising help for such applications due to their high stability under atmospheric conditions. Modeling phase equilibria of semiclathrate hydrate systems is an important prerequisite for their practical application in several fields. Several researchers [20−28] have modeled gas hydrate systems either in pure state or in the presence of thermodynamic inhibitors. Most of the authors used PatelTeja (PT) Equation of State (EoS) for their modeling work to develop various correlations pertaining to various properties like fugacity of the gas phase, critical temperature and pressure, etc. Klauda and Sandler [29] proposed a classical thermodynamic model for the equilibrium pressures for different guests of structure I and II gas hydrate systems. They stated that their model [29] removed the need for reference energy parameters used in the van der Waals and Platteeuw (vdWP) type models. They computed Langmuir constants by fitting the intermolecular potentials between the gas molecules to ab initio quantum mechanical energies. Yoon et al. [30] published an improved and generalized model to predict the dissociation pressures of hydrate forming systems of pure gases and multi-component gas mixtures. Based on the van der Waals-Platteeuw theory with the Kihara spherical-core potential function, a new equation for the water fugacity in the filled hydrate phase was provided. The fugacities of all components in vapor and liquid phases coexisting with hydrates were calculated by the Soave-Redlich-Kwong (SRK) equation of state incorporated with the modified Huron-Vidal secondorder mixing rule [30]. Zhang et al. [24] developed a simple thermodynamic model with only two adjustable parameters which can accurately correlate hydrate-liquid water-vapor phase equilibrium for single-guest gas hydrates at temperatures below 300 K. The approach combines the van der WaalsPlatteeuw theory and the Peng-Robinson (PR) EoS and provides a unified treatment of the two fluid phases (liquid water and hydrocarbon). Tavasoli et al. [28] used Elliott-SureshDonohue EoS coupled with van der Waals-Platteuw model to get the phase behavior of gas hydrate system both in the presence and absence of inhibitors. Mainusch et al. [31] conducted experiments and also modeled the methane gas hydrate system in water and acetone mixture. In their study, the thermodynamic model introduced by Moshfeghian and Maddox [32] was applied to predict accurately hydrate formation temperatures in the presence of hydrate suppressants such as

methanol and ethylene glycol. Bahadori et al. [33] developed a simple-to-use correlation for accurate prediction of hydrate forming pressures of pure alkanes in the presence of different hydrate inhibitors. Their correlation was applied for predicting methane hydrate formation conditions in the presence of inhibitors with weight percentages up to 50%, 40%, 30%, and 25% for methanol, ethylene glycol, and sodium chloride solution, respectively. Chen and Guo [34] proposed a semiempirical model for the modeling of pure gas hydrate system. They used Patel-Teja EoS for developing correlation between the fugacities of the gas phase and the gas hydrate under equilibrium conditions. The author proposed a two-step mechanism for the formation of the gas hydrates. They validated their model with the experimental data on phase equilibria of binary gas mixtures and reported it matching very well with the experimental results [35]. It is observed that the Chen and Guo’s model is simple, concise and more flexible to apply not only for clathrate system of pure gases and gas mixtures but also for hydrate systems in presence of inhibitors [36,37]. Chen and Guo’s model, thus, shows potential to be extended for semiclathrate hydrate system. Even though the modeling of gas hydrate system has progressed in recent past, there is no effort in an open literature to model semiclathrates system, which has potential application in gas storage and transportation, geo-sequestration, and separation of gases from flue gases. In this study, the model of Chen and Guo [34,38] is extended for predicting phase equilibria of semiclathrate hydrate of gases in aqueous solution of TBAB. A correlation to predict the activity of water in the presence of varying concentrations of TBAB was formulated in a similar way as Mainusch et al. [31] did and used along with Chen and Guo’s model. The extended model was then applied to various systems of semiclathrate hydrates of gases in aqueous solution of TBAB. The model predictions were observed to be in accordance with the literature data [7,11,14]. Additionally, a correlation has been developed for semiclathrate hydrate systems for hydrates promotion temperature in the presence of TBAB. This correlation is similar to that proposed by Hammerschmidt [39] for gas hydrate suppression temperature in the presence of an inhibitor. 2. Thermodynamic modeling The model of Chen and Guo [34,38], as used in this study, is based on two-step mechanism for gas hydrate formation. The basic principal underlying this model is the two steps for the formation of gas hydrate structure, which mainly include a quasi-chemical reaction process to form basic hydrate structure followed by an adsorption of smaller gas molecules in the linked cavities of basic hydrate. The new concepts proposed thus develop concepts related to local stability, linked cavity, and basic hydrate. Extensive test results indicate that the model of Chen and Guo is adequate for predicting the hydrate formation conditions for pure gases and gas mixtures [35,36]. In this work, the basic model of Chen and Guo [34,38] is extended to the semiclathrates of pure gases in aqueous TBAB solution.

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Chen and Guo [34] described the hydrate formation process by the following simple reaction: H2 O + λ2 G → Gλ2 · H2 O

(1)

where, G and λ2 represent the gas species and the number of gas molecules per water molecule in the basic hydrate structure, respectively. To get the equilibrium phase conditions, Chen and Guo [34] equated the fugacity of gas phase, f , and fugacity of hydrate structure, f o , using the following final form: α

o

f = f (1 − θ)

(2)

expected using more sophisticated EoS which are now available in an open literature, viz., ESD EoS, CPA EoS or VPT EoS [28,40,41]. However, in this work we restrict ourselves using SRK EoS due to its wide acceptance for hydrocarbon mixtures. SRK EoS has the following form: RT aσ − V − b V (V + b)  σ = [1 + m(1 − Tr )]2

P=

m = 0.480 + 1.574ω − 0.176ω 2

where, α = λ1 /λ2

(3)

where, λ1 and λ2 are the number of linked cavities per water molecule in the basic hydrate and the number of gas molecules per water molecule in the basic hydrate, respectively; θ is the fraction of linked cavities occupied by the gas molecules and defined as Cf θ= (4) 1 + Cf C is theLangmuiradsorption coefficient and is given by Y ; T is the system temperature in K; C = X exp T −Z X, Y and Z are the Antoine constants. If the value of θ in Equation 4 is zero, then f = f o , thus denoting that f o is the fugacity of gas phase with unfilled basic hydrate. Chen and Guo [34] used the following form for f o to calculate the fugacity of basic hydrate structure f o = f o (T )f o (P )f o (aw )

(5)

where, 

B T − C   βP o f (P ) = exp T

f o (T ) = A exp

−1/λ2

f o (aw ) = aw

 (6) (7) (8)

where, P is the system pressure; aw (in Equations 5 and 8) is the activity of water; A , B and C in Equation 6 are the Antoine constants and β (in Equation 7) is the structural parameter defined as ΔV (9) β= λ2 R The gas phase fugacity is calculated from the equation of state (EoS). Chen and Guo [34] used Patel-Teja (P-T) EoS to calculate gas species fugacity. However, in our previous study [36] we observed that SRK EoS is more useful than P-T EoS to predict the gas hydrate behavior at high pressure condition of above 5 MPa. Therefore, in this study, we use SRK equation of state for calculating the gas species fugacity. It is to be noted here that similar or better predictions may be

a = ϕa

R2 Tc2 Pc

(10) (11) (12) (13)

RTc (14) Pc Tr is the reduced temperature; Pc and Tc are the critical pressure and temperature, respectively; ω is the acentric factor; V is the molar volume of gas; and the constants, φa and φb have values 0.42747 and 0.08664, respectively, for all pure gases. After introducing the compressibility factor ‘Z’ into the SRK EoS and replacing molar volume V by ZRT /P , Equations 10–14 can be modified to b = ϕb

Z 3 − Z 2 + (A − B − B 2 ) − AB = 0 A=

aσP (RT )2

(15) (16)

bP (17) RT where, R is the universal gas constant. Chen and Guo [34] found values of α and β (in Equations 2 and 7, respectively) only suitable for pure gas hydrates of structure I and structure II. In fact, the semiclathrate hydrates of TBAB show different structural morphology as compared with the pure gas hydrate [4−6]. Several researchers [42−45] observed two types of structures, viz., A and B for varying TBAB concentrations. However, it is also observed from these literatures that at a critical weight percentage of 18 wt%, type B has higher melting point, while above 18 wt%, type A has higher melting point. We, therefore, believe that up to a TBAB weight percentage of 18 wt%, the phase equilibrium point of semiclathrate hydrate is decided by melting of type B structures, while at above 18 wt%, it is decided by melting of type A structure. We observe that the structural constant β depends on the weight fraction of TBAB in the system; whereas the structural constant α is found to depend on the basic hydrate lattice and also on the amount of the TBAB in the system. We, therefore, calculate the values of α, under two situations, below and above 18 wt% of TBAB concentration. These values are given in Table 1. It is also found that the structural constants α and β are independent of the guest gas, i.e., the values of α and β are found to be the same for methane, carbon dioxide and nitrogen semiclathrate hydrates provided the concentration of TBAB in all the three systems is the same. The value of α is obtained using Equation 3. Wherein, λ1 is the number B=

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of linked cavities per water molecule in the basic hydrate and λ2 is defined as the number of gas molecules per molecule of water. In semiclathrate structure of TBAB, one TBAB and 38 H2 O molecules form hydrate structure. The semiclathrate structure is a combination of face centered cubic (FCC) and body centered cubic (BCC); the linked cavities are found to be 1.75 for type B and 1.65 for type A after taking into consideration the co-ordination number for FCC and BCC structures, which gives λ1 1.75/38 for type B and 1.65/38 for type A. Additionally, in semiclathrate hydrate of TBAB, there are 3 guest gas molecules per 38 molecules of water [4,5], which means λ2 equals 3/38. The values of β, which are independent of the type of guest gas molecule but depend on the TBAB concentration, are obtained as a best fit value with the experimental data on phase equilibria of semiclathrate hydrate systems (see Table 1) and the same were used in this work. The values of thermodynamic parameters, such as, critical temperature and critical pressure, Antoine constants and acentric factor are chosen from the literature appropriately depending on the nature of guest gas molecule in semiclathrate hydrate [46]. Table 1. Structural parameters α and β for semiclathrate hydrate system of TBAB TBAB concentration (wt%) 5 10 20 30 42.7

Structural parameter α 1.75/3 1.75/3 1.65/3 1.65/3 1.65/3

Structural parameter β (K/bar) 0.697 0.45 0.35 0.30 0.22

Chen and Guo’s model [34] assumed the activity of water as unity for all the system temperatures and sample gas system. However, in semiclathrates system containing TBAB, its solubility in water is much higher than that of the gas and hence the change in activity of water due to TBAB is much higher than that caused by the gas. We presume that the activity of water is a function of the TBAB concentration in the system and also a function of the system temperature. Mainusch et al. [31] have shown that the activity of water can be calculated as a function of temperature from the below equation:   ΔH 1 1 ln aw = (18) − nR T1 T0 where, ΔH is the enthalpy of hydrate formation; T1 is the hydrate formation temperature in the presence of a suppressant; T0 is the hydrate formation temperature of pure water. In this work, an extension of the above equation is proposed which incorporates the concentration dependence of TBAB on the activity of water and has the following form:   1 k1 aw = − k2 (19) exp 1 − xT T where, k1 and k2 are the constants and depend on the nature of guest gas molecules. xT is the mole fraction of TBAB in the system. Constants, k1 and k2 , are considered as tuning parameter due to the absence of thermodynamic data on

TBAB-water-gas system. We can use the other data on the salt system to tune the value for TBAB-water system. However, as mentioned, the data for the activity of water-TBAB system were not found in an open literature, and thus the activity data available for various water-salt systems were studied. From the available data [47], ZnBr2 salt system with the highest molecular weight which is close to TBAB salt system amongst the various salts available is used as starting guess and finely tuned. Therefore, we use data on the activity of water in the presence of a sample salt system, namely, zinc bromide (ZnBr2 ), to get an initial guess on k1 and k2 . The initial guess values of these constants were obtained after performing least-square regression analysis of the experimental data for [water+ZnBr2] system [47], respectively. These values of [water+ZnBr2] system were observed to be 409.6257 and 3.9159 [47]. However, in the current semiclathrate hydrate system, due to the addition of a third gas component as a guest molecule in the basic semiclathrate structure, the activity of water in the presence of salt may change possibly due to the solubility of gas into water [34]. The initial guess values of the constants k1 and k2 are, therefore, tuned for the semiclathrates of gases in aqueous TBAB solution. For semiclathrate hydrate of methane and carbon dioxide, data on phase equilibrium at 5 wt% TBAB were used to tune these parameters. With the tuned model parameters, the model was run and the model results were compared with the available experimental data for high concentrations of TBAB to check the robustness of the model. For the case of semiclathrate hydrate of nitrogen, only one data set corresponding to 10 wt% TBAB is available, which was used for tuning and model validation. The final tuned values for TBAB-water-gas system are given in Table 2. It is also to be noted that the correlation proposed in Equation 19 is applicable only for TBAB-water-gas system. Table 2. Constants for calculating activity of water in the presence of TBAB in semiclathrate hydrate system Gas Methane Methane Methane Methane Carbon dioxide Carbon dioxide Carbon dioxide Nitrogen

TBAB (wt%) 5 10 20 30 5 10 42.7 10

k1 3650 3673 3710 3722 719 724 725 5110

k2 12.640 12.640 12.640 12.640 2.705 2.705 2.705 17.735

3. Results and discussion The flow chart to solve the set of model equation is shown in Figure 1. The model equations as described above along with the correlation of activity of water in TBAB system were solved using a code generated using MatLab . The model predictions are developed for semiclathrate hydrate systems of aqueous solution with varying concentration of TBAB and having three different gases as a guest molecule. These are, namely, CH4 , N2 and CO2 . The model predictions for these

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systems are shown in Figures 2–4. Experimental data available on the phase equilibria for three different systems of semiclathrate hydrates of gases are taken from the open literature [7,11,14] for comparison. The experimental data on phase equilibria of pure gas hydrate system for methane [48], carbon dioxide and nitrogen [1] are also shown for comparison. The model predictions are observed to be in good agreement with the experimental data in all the three cases. The experimental data on phase equilibria for methane semiclathrates hydrates are available up to 15 to 25 MPa for varying concentration of TBAB for comparison [11], while for

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carbon dioxide and nitrogen up to 7 MPa and 25 MPa, respectively [7,11,14]. The model predictions of semiclathrate hydrate model are restricted to the available experimental data range for the systems studied. It is observed from Figures 2–4 that as the equilibrium formation pressure and temperature increases, the model predictions show parallel shift from the pure gas hydrate phase equilibrium curve. It is observed from Figure 2 that as the concentration of TBAB in the system increases the formation temperature of the methane semiclathrate hydrates increases as compared to pure methane gas in water system (pure natural gas hydrates case) at the same system pressure. The two different values of structural constant, α (as listed in Table 1) do not have appreciable change in model predictions using two values. Similar observation can be seen from Figures 3 and 4 for semiclathrate hydrates of carbon dioxide and nitrogen as compared to their pure gas hydrate states. It is to be pointed out here that the solid line in Figure 3, which is actually the predictions of Chen and Guo’s model [34] for pure gas hydrate system of CO2 , shows less accuracy at lower pressure. However, the model developed in this work for semiclathrate hydrate system shows good match with the

Figure 2. Phase equilibria of semiclathrates of methane in TBAB aqueous solution. Experimental values are shown by symbols and model predictions by lines

Figure 1. Flow chart for calculation of phase equilibria of semiclathrate hydrate system

Figure 3. Phase equilibria of semiclathrate hydrate of carbon dioxide in TBAB aqueous solution. Experimental values are shown by symbols and model predictions by lines

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least-square method of regression analysis (R2 = 0.95) for the range of pressure as mentioned. The observed values of C1 for methane, nitrogen and carbon dioxide are 13812.98, 95133.97 and 18082.14, respectively. These values were then used to calculate the prediction of proposed correlation as shown as in Equation 21 for range of pressures. (ΔT )exp, avg is obtained as an average value of (ΔT )exp for a range of pressures. These are given in Table 3. It is observed from Table 3 that the proposed correlation is able to predict the promotion effect quite satisfactorily for a range of pressures mentioned and for several concentrations of TBAB in semiclathrate hydrate systems. This correlation, therefore, can be useful for practical applications related to semiclathrate hydrate systems. Figure 4. Phase equilibria of semiclathrates of nitrogen in aqueous solution of TBAB. Experimental values are shown by symbols and model predictions by lines

experimental values (see dotted lines) even under low pressure condition for the CO2 system. This clearly shows that TBAB acts as a thermodynamic promoter. Hammerschmidt [39] reported the following form of equation for predicting the hydrate suppression temperature, (ΔT )s , for gas hydrate of natural gases in the presence of methanol: 1297W (ΔT )s = (20) M (100 − W ) Lee and Kang [49] used the above equation for predicting the natural gas hydrate suppression temperature for other inhibitors such as, ethylene glycol, sodium chloride and methanol. In similar efforts, to develop a correlation for the hydrate promotion temperature, (ΔT )p , of semiclathrate hydrates system of TBAB, we propose the following form of equation C1 W (ΔT )p = (21) M (W − 100) where, (ΔT )p is the change in temperature due to promotion effect; W is the weight percentage are of TBAB in the system and M is the molecular weight of TBAB. C1 is a constant and is observed to be different for different guest gas molecules in semiclathrate hydrate system. To get the value of C1 , we first calculated (ΔT )exp = (Ti, exp, pure gas hydrate − Tj, exp, semiclathrates ) and (ΔT )mod = (Ti, exp, pure gas hydrate − Tj, model, semiclathrates ) under a fixed pressure and a fixed percentage of TBAB. In the expression for (ΔT )exp , i indicates the respective experimental temperature value for pure gas hydrate system, while j indicates the respective experimental value for the semiclathrate hydrate system. In the expression of (ΔT )mod, i indicates the respective experimental temperature value for pure gas hydrate system, while j indicates the respective model value for the semiclathrate hydrate system. The experimental values are taken from elsewhere [1,7,11,14]. One should note that we keep Ti, exp of pure gas hydrate system at a corresponding pressure as a reference values for both (ΔT )exp and (ΔT )mod . The obtained values of (ΔT )exp and (ΔT )mod are then used to calculate C1 using

Table 3. Hydrate promotion temperature of semiclathrate hydrate system of gases in the presence of TBAB Guest gas molecule in semiclathrate Methane

TBAB Pressure (ΔT )exp, avg (ΔT )p, avg concentration limits (K) (K) W (wt%) (MPa) 5 4.688−15.858 4.25 2.255 10 4.482−35.853 5.5 4.760 20 3.310−15.434 9.46 10.712 30 3.283−17.400 15.36 18.363 45 3.142−4.126 32.33 35.056 Carbon dioxide 5 2.860−4.716 4.70 2.952 10 1.472−4.242 9.52 6.232 42.7 1.365−3.452 34.89 41.780 Nitrogen 5 17.530−33.940 14.11 15.532

4. Conclusions Chen and Guo’s model has been extended for a semiclathrate hydrate system of gases in aqueous TBAB solution. We observed that the activity of water was a function of TBAB concentration in the system, nature of guest gas molecule and also a function of the system temperature. We, therefore, proposed a correlation for the activity of water with TBAB and guest gas molecules to be applied for semiclathrate hydrate system. The developed model was found to predict the phase equilibria of semiclathrate hydrate system satisfactorily. Additionally, a new correlation has been proposed for the hydrate promotion temperature of semiclathrate hydrate systems of TBAB, which is able to predict the promotion effect quite satisfactorily for a range of pressures studied from the literature values. Acknowledgements Authors would like to acknowledge the office of the Industrial Consultancy and Sponsored Research (ICSR), Indian Institute of Technology Madras, Chennai for financial support through project number OEC/10−11/530/NFSC/JITE and the National Institute of Ocean Technology (NIOT), Chennai, India, through grant; OEC/1011/105/NIOT/JITE. Nomenclature α fractional coefficient β structural parameter θ fraction of linked cavities occupied by the gas molecules

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λ1 λ2 ω aw ϕa ϕb σ f fo k1 , k2 xT A , B , C X, Y , Z G M P Pc Pr R T0 T1 T Tc Tr V W Z

number of linked cavities per water molecule in the basic hydrate number of gas molecules per water molecule in the basic hydrate structure acentric factor activity of water parameter in SRK EoS parameter in SRK EoS parameter in SRK EoS fugacity of gas phase, MPa fugacity of hydrate structure, MPa constants in Equation 19 mole fraction of TBAB Antoine constants Antoine constants gas species molecular weight of TBAB, g/mol system pressure, MPa critical pressure, MPa reduced pressure, P/Pc universal gas constant hydrate formation temperature of pure water, K hydrate formation temperature in the presence of a suppressant, K system temperature, K critical temperature, K reduced temperature, T /Tc molar volume of gas, m3 weight percentage of TBAB compressibility factor

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