Phase Equilibrium of Methane Hydrate in the Presence of Aqueous

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

pubs.acs.org/jced

Phase Equilibrium of Methane Hydrate in the Presence of Aqueous Solutions of Quaternary Ammonium Salts Pawan Gupta, Vishnu Chandrasekharan Nair, and Jitendra S. Sangwai* Gas Hydrate and Flow Assurance Laboratory, Petroleum Engineering Program, Department of Ocean Engineering, Indian Institute of Technology Madras, Chennai-600 036, India S Supporting Information *

ABSTRACT: Families of various quaternary ammonium salts (QAS) have been of great interest to gas hydrate based investigations. In this work, an attempt has been made to understand the effect of QAS of the bromide family with increasing alkyl chain length, such as tetra-methyl, tetra-ethyl, and tetra-butyl ammonium bromide (TMAB, TEAB, and TBAB) at two different concentrations (0.05 and 0.1 mass fraction) in an aqueous solution on the hydrate−liquid−vapor (H-L-V) phase equilibrium of the methane hydrate system. Various experiments were performed to capture phase equilibrium data in the equilibrium pressure range of 7.6−4.2 MPa and temperature range of 282.4−276.8 K. It has been observed that the addition of TMAB and TEAB shifts the phase equilibrium curve of methane hydrate to higher pressure and lower temperature conditions. TMAB and TEAB have shown thermodynamic inhibition unlike TBAB which has shown a promotion effect. The Clausius−Clapeyron equation is used to calculate the enthalpy of dissociation of methane hydrate in various QAS aqueous solutions to examine the effect of QAS on methane hydrate structural information. The electrical conductivity measurements were also made to correlate the hydrate inhibition effectiveness of QAS on methane hydrate system. In addition, a phase equilibrium model has been extended to predict the phase behavior of methane hydrate + (TMAB, TEAB, or TBAB) aqueous solutions for a total 91 experimental phase equilibrium data points obtained from this work and the literature. The absolute average relative deviation in equilibrium pressure (AARD/P (%)) observed from the proposed model with the experimental equilibrium pressure data produced in this work and from several sources in the literature have been observed to lie within ±3.2%, indicating the robustness of the model.

1. INTRODUCTION Gas hydrates are crystalline compounds which are formed due the encapsulation of “guest” gas molecules, such as methane (CH4) and ethane (C2H6), etc., into the cages formed by “host” water molecules under low temperature and high pressure conditions.1 Interactions between the host and guest molecules give rise to the formation of different structures such as sI, sII, and sH. Formation of these structures depends on the ratio of the diameter of the cage and the size of guest gas molecules. There would be no hydrate formation if the guest gas size is bigger than the free cage diameter.1 Gas hydrates have been recognized as a nuisance to the oil and gas industry as they form in the oil and gas pipelines restricting the fluid flow thereby increasing flow assurance issues.2 With the advent of research, gas hydrates may also play a vital role in numerous industrial applications such as natural gas storage, multicomponent gas separation, seawater desalination, carbon dioxide sequestration, and air conditioning applications.3−7 Natural gas should be cleaned for any impurities such as natural gas liquids, carbon dioxide (CO2), hydrogen sulfide (H2S), and water vapor and should be stored efficiently and economically at lower volumes before it can be transported to the customer.8 In addition to liquefied natural gas, natural gas © XXXX American Chemical Society

can also be transformed into solid gas hydrates for possible storage and transportation applications. Gas separation, storage, and transportation using hydrate technology has not yet been practical because the hydrate formation conditions are relatively at higher pressures and much lower temperatures which are unsuitable for such applications. Semiclathrate hydrates (SCHs) are analogous to gas hydrate and can be explored for such applications more efficiently. As compared to pure gas hydrate systems, semiclathrate hydrates can be formed at relatively low pressure conditions at a given temperature.9−11 SCHs have been recognized to perform like a sieve for different sized gas molecules and can help in the separation of multicomponent gas mixtures.12,13 Tetra-butyl ammonium bromide (TBAB) from a family of tetra-alkyl ammonium halide has been recognized to form semiclathrate hydrates at moderate pressure and temperature conditions. In the SCH of TBAB, the anion of TBAB (i.e., Br−) forms a hydrogen bond with water molecules and generates a water−anion host Special Issue: Emerging Investigators Received: November 9, 2017 Accepted: January 19, 2018

A

DOI: 10.1021/acs.jced.7b00976 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Details of the Materials Used in This Studya no.

chemical name

chemical formula

molecular weight (g/mol)

purity (weight fraction)

source

1 2 3 4

tetramethylammonium bromide (TMAB) tetraethylammonium bromide (TEAB) tetrabutylammonium bromide (TBAB) methane

C4H12BrN C8H20BrN C16H36BrN CH4

154.05 210.16 322.37 16.04

0.99 0.99 0.99 0.99

Loba Chemie Mumbai Loba Chemie, Mumbai Sisco Research Laboratories, Mumbai Bhuruka Gas Agency, Bangalore

a

Deionized water has been used in all experiments.

framework.14 The TBAB SCH structure consists of larger cages (two tetrakaidecahedra cages and two pentakaidecahedra cages) and smaller (dodecahedra) cages. The cation of TBAB (TBA+) rests in the larger cages of the SCH structure, whereas the smaller cages remain unoccupied. The smaller cages are found to be ideal for methane gas to sit in with stability. Hydrogen being much smaller will not be captured because of instability.15 The dodecahedron cavities (smaller cages) permit only smaller sized guest gas molecules (less than 5 Å in diameter) to rest inside while it discards larger sized guest gas molecules [e.g., ethane (5.5 Å); propane (6.3 Å); i-butane (6.5 Å).16 The phase equilibrium of the methane gas + TBAB hydrate system is vital for methane gas storage and the gas separation process. Aladko and co-workers17,18 performed a study on phase equilibrium of simple binary system of quaternary ammonium salts (QASs), such as tetra-methyl/tetra-ethyl/tetra-propyl ammonium bromide (TMAB/TEAB/TPrAB) and water by differential thermal analysis. They suggested that every cation of a quaternary ammonium salt has its own tendency to form a water structure around it. TMAB and TEAB form a metastable hydrate due to the high strength of the crystal structure of the salt.18 Tetra-methylammonium bromide forms a polyhedral structure, whereas tetra-ethylammonium bromide forms a layertype framework. A hydration number of 4 is observed for both TMAB and TEAB hydrate. Also, hydrates with a hydration number of 5 (TMAB) and 7.7 (TEAB) have been observed.18 Nilson and his team19 investigated an interaction of water with cations of QASs, namely tetra-methylammonium bromide cation (TMA+), and tetra-ethylammonium bromide cation (TEA+). It was reported that the cation of the QASs acts as a structure director due to their apolar nature. Furthermore, the apolar nature increases with increase in the chain length of the QASs. They also reported that the lower alkyl chain of the QASs acts as a facilitator in growth, while higher alkyl chain acts as a nucleating agent in the synthesis of zeolite. Very few studies have been reported for methane hydrate formation in the presence of varying alkyl chain length of QASs in an aqueous solution. Recently, Su and co-workers20 have investigated the phase equilibrium of methane hydrate + QASs aqueous solutions, such as TMAB, TEAB, TPrAB, TPeAB, and TBAB. TMAB, TEAB, and TPrAB were investigated at a single concentration (0.62 mol %), whereas TPeAB and TBAB were studied at two different concentrations (0.294 mol % and 0.62 mol %). They reported that the alkyl chain length of the quaternary salt of ammonium bromide affects the phase stability of methane hydrate. The presence of TMAB, TEAB, or TPrAB slightly inhibits, whereas TPeAB and TBAB promotes the methane hydrate phase equilibrium. The hydrate−liquid−vapor (H-L-V) phase equilibrium of the SCH of methane in TBAB aqueous solution has widely been studied in recent times. 9−11,21−24 However, the phase equilibrium of methane hydrate in TMAB and TEAB aqueous solutions (which is within the same family of QASs but with

lower alkyl chain length) have not been well understood, which otherwise could shed light on the effect of alkyl chain length of the QASs on the phase behavior of methane hydrate. As mentioned above, the cation of tetra-alkyl ammonium bromide has an ability to transform the structure of water around it. The charged moieties of salts have bearing on controlling the structure of a given system and may function as an inhibitor or promoter (both, as thermodynamic and kinetic inhibitor). Understanding the phase behavior of methane hydrate + aqueous solutions of QASs (such as TMAB, TEAB, or TBAB) is very important to understand the effect of alkyl chain length (cation) on methane hydrate phase equilibrium and would be an interesting fundamental research investigation. In this work, an attempt has been made to understand the effect of the QASs of the bromide family with increasing alkyl chain length (TMAB, TEAB, and TBAB) at two different concentrations (0.05 and 0.1 mass fraction) in an aqueous solution on the HL-V phase equilibrium of methane hydrate system. Various experiments were executed to capture phase equilibrium data in the equilibrium pressure range of 7.6−4.2 MPa and temperature range of 282.4−276.8 K. The Clausius−Clapeyron equation has been used to calculate the enthalpy of dissociation of methane hydrate in the presence of various QAS aqueous solutions to examine the influence of QASs on methane hydrate structural information. The electrical conductivity measurements were also made to correlate the inhibition effectiveness of QASs on the methane hydrate system. In addition, a phase equilibrium model from our previous work25 has been extended to predict the phase behavior of methane hydrate + (TMAB, TEAB, and TBAB) aqueous solutions.

2. EXPERIMENTAL SECTION 2.1. Materials. Methane gas with a purity 99.95% (provided by Bhuruka gas agency, Bangalore) is used for the experimental work. All samples were prepared using deionized water acquired from Labostar (SIEMENS, Germany). An analytical weighing balance (Radwag AS-220/X) is used for measuring the chemicals. The weighing balance works with an uncertainty of ±0.00004 mass fraction (mf). The details on the chemicals, their concentrations, and nomenclature have been provided in Table 1. 2.2. Experimental Setup. A hydrate rector as illustrated in Figure 1 was used for measuring methane hydrate equilibrium.25,26 The setup comprises a 250 mL high-pressure reactor made up of SS-316 with an operational pressure of 10 MPa. A jacket encloses the reactor so that a water + glycol mixture from the water bath can be circulated through it to control the temperature of the reaction mass at the desired condition using a Thermo Haake water bath (model A 25). The temperature and pressure of the reaction mass within the reactor were recorded using a pressure transmitter (model Wika A-10) and a high-precision temperature sensor (model Pt-100). These calibrated sensors work with an uncertainty in B



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Figure 2. A sample isochor obtained during methane hydrate formation in the presence of an aqueous solution of TEAB at 0.05 mass fraction (this work). Figure 1. Schematic diagram of the experimental setup used in this study.

experiments (see Table 2) have been performed at different initial pressures to generate the phase equilibrium curve. Table 2. Experimental Phase Equilibrium Data on Methane Hydrates in the Presence of Aqueous Solutions of TMAB and TEABa

the pressure and temperature in the range of ±0.005 MPa and ±0.05 K, respectively. A magnetic torque-stirrer is used to agitate the mixture within the reactor. In addition, a syringe pump (500 D, Teledyne Isco, USA) is deployed to augment the pressure of the gas injected into the reactor. A data acquisition system records pressure and temperature at 30 s sampling time into the computer for further study. 2.3. Experimental Procedure. Before the start of the experiment, the reactor is cleaned and washed with deionized water to eliminate undesired particles and dried. Phase equilibrium experiments of methane hydrate + various QAS aqueous solutions (as in Table 1) have been performed individually each time with fresh QAS samples. Aqueous solutions (160 mL) of various QAS chemicals with the desired concentration is then filled into the reactor during each experiment. Thereafter, the reactor is fastened and purged twice with methane gas (at about 0.5 MPa each time) to remove atmospheric air within the reactor. Then, methane gas is injected into the reactor at a fixed value of experimental pressure (say 7.5 MPa). The reaction mass within the reactor is stirred using a magnetic torque stirrer at 1000 rpm. After the pressure in the reactor is stabilized, the cold water from the water bath is circulated through the jacket of the reactor so as to cool the reaction mass up to 268.15 K. To measure the hydrate phase equilibrium, the isochoric pressure search method was used as shown in Figure 2.27 Figure 2 shows sample isochor obtained during methane hydrate formation in a TEAB (0.05 mass fraction) aqueous solution. It has been observed that the pressure inside the reactor decreases with a decrease in temperature due to shrinkage of gas (from a to b), followed by a rapid drop in pressure (from b to c). This rapid drop in pressure (from b to c) accompanied by an exothermic process shows the start of the methane hydrate nucleation and growth. After adequate hydrate formation in the reactor, the reactor is heated (from c to d) followed by very slow heating (from d to e) at the rate of 0.1 to 0.2 K/h in order to accurately determine the phase equilibrium of hydrate system. The phase equilibrium of the methane hydrate + QAS aqueous solutions is then determined by the intersection of the slope of the threephase (H-L-V) dissociation curve and two-phase (V-L) shrinkage curve near the equilibrium point.26−28 Several such

TMAB 0.05 mf

TEAB 0.10 mf

0.05 mf

0.10 mf

T/K

P/MPa

T/K

P/MPa

T/K

P/MPa

T/K

P/MPa

282.4 280.5 278.8 277.7

7.60 6.24 5.40 4.77

281.4 280.9 279.7 278.0 276.9

7.30 6.94 6.02 5.01 4.27

282.5 281.8 280.7 279.2 277.3

7.42 6.92 6.13 5.53 4.54

282.1 280.5 279.0 277.1

7.39 6.43 5.40 4.55

a

Expanded uncertainties (includes instruments and experimental measurements): U(P) = ± 0.05 MPa, U(T) = ± 0.1 K, U(mass fraction) = ± 0.0001 (0.95 level of confidence). Total number of experiments are 18.

3. RESULTS AND DISCUSSION Initially, the phase equilibrium of the pure methane gas hydrate was investigated and compared with experimental data available in the literature29 to confirm the reliability of the experiments. Subsequently, the phase equilibrium of methane hydrate + QAS aqueous solutions has been presented. Information on the enthalpy of dissociation of methane hydrate in the presence of various QAS aqueous solutions is calculated using the Clausius−Clapeyron equation. Subsequently, information on the electrical conductivities of QAS aqueous solutions measurements is provided to understand its effect on methane hydrate inhibition. Then, a thermodynamic phase equilibrium model is discussed in detail. 3.1. Experimental Validation. Initially, a few experiments were performed to validate the experimental setup and procedures. For this, the phase equilibrium studies were performed on a pure methane hydrate system. Figure 3 shows that the phase equilibrium experimental data of pure methane hydrate match well with the literature data.29 Thus, the reliability of the experimental procedure and the reactor used for the hydrate study has been confirmed before new experiments are started. C



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chain length of ionic liquids inhibit hydrate more than the longer alkyl chain length ionic liquids.30−33 It can also be observed from Figures 3a and 3b that TBAB has a pronounced promotion effect on methane hydrate system and forms a reasonably stable hydrate at higher temperature and lower pressure conditions. The reason for getting different phase behavior for different methane hydrate + QAS systems may be due to guest and host interactions, change in the activity of water due to TBAB present in an aqueous solution, and formation of unusual water cages by larger TBAB guest molecules than the TMAB and TEAB systems.6 In a recent study by Su and co-workers,20 the methane hydrate inhibition in the presence of TMAB and TEAB is accounted for by considering it as a colligative property. It has been said that the methane hydrate inhibition in the presence of TMAB and TEAB aqueous systems is similar to that of NaCl. While the methane hydrate promotion effect of TBAB is due to the formation of unusual cages with water molecules, TMAB and TEAB may not have participated in any structural changes (semiclathrate hydrate formation) unlike TBAB. 3.2.1. Enthalpy of Dissociation of Methane Hydrate + QAS Systems. Enthalpy of dissociation of methane hydrate in the presence of TMAB, TEAB, and TBAB aqueous solutions at 0.05 mf and 0.1 mf has been determined to analyze any structural information. It has been observed that the enthalpy of dissociation of hydrate can provide insights into the strucural information.1,34 The amount of energy released in “kilojoules” when one mole of hydrate is being dissociated is known as enthalpy of dissociation and is being calculated using the wellknown Clausius−Clapeyron equation as shown in eq 1:1

Figure 3. Phase equilibrium of methane (CH4) hydrate in the presence of TMAB, TEAB, and TBAB aqueous solutions. Experimental points: △, pure CH4 hydrate (this work); ▲, pure CH4 hydrate, Gayet et al.29 (a) □, 0.05 mf TMAB (this work); ○, 0.05 mf TEAB (this work); ◊, 0.05 mf TMAB, Su et al.;20 ∗, 0.0679 mf TEAB, Su et al.;20 ●, 0.05 mf TBAB, Arjmandi et al.;10 ×, 0.05 mf TBAB, Sangwai and Oellrich.11 (b) +, 0.01 mf TMAB (this work); , 0.01 mf TEAB (this work); ■, 0.01 mf TBAB, Arjmandi et al.;10 ∗, 0.01 mf TBAB, Mohammadi et al.5

ΔHd d(ln P) =− d(1/T ) ZR

(1)

where ΔHd is the enthalpy of dissociation (kJ·mol−1), P is the pressure (MPa), T is the temperature (K), Z is the compressibility factor (obtained by Peng−Robinson equation of states35) and R denotes the universal gas constant (m3 MPa K−1 mol−1). To infer ΔHd, the phase equilibrium data of methane hydrate systems in various QAS aqueous solutions were plotted on a semilogarithmic plot with pressure (P) on the ordinate and reciprocal of temperature (1/T) on the abscissa. The values of ΔHd calculated from eq 1 are shown in Table 3. Interestingly, there is no substantial difference between the value of ΔHd obtained for methane hydrate in the presence or absence of TMAB and TEAB. This indicates that the addition

3.2. Phase Equilibrium of Methane Hydrate + QAS Aqueous Solutions. Table 2 shows the detail on the concentrations of QAS used and the experimental phase equilibrium data for methane hydrate + TMAB/TEAB aqueous solutions generated in this work. Two concentrations (0.05 mf and 0.1 mf) of TMAB/TEAB were used. Figure 3a shows phase equilibrium of methane hydrate in the presence of 0.05 mf of TMAB/TEAB/TBAB aqueous solutions, while Figure 3b shows methane hydrate phase equilibrium in the presence of 0.1 mf of TMAB/TEAB/TBAB aqueous solutions obtained in this work. Phase equilibrium data on methane hydrate + (TEAB, TMAB, and TBAB) aqueous solutions with varying concentrations have also been used and compared from various literature.5,10,11,20 The results on 0.05 mf of TMAB and TEAB obtained in this work are in good agreement with those obtained by Su and co-workers.20 It has been observed from Figure 3 that TBAB shows significant hydrate promotion, while TMAB and TEAB show hydrate inhibition. The magnitude of inhibition in the case of TMAB aqueous solution is slightly more as compared to TEAB at 0.05 and 0.1 mf. The average temperature depression (ΔT for hydrate inhibition) observed for TMAB and TEAB at 0.05 mf are 1.20 and 1.01 K, and at 0.1 mf are 1.55 and 1.08 K, respectively. As said above, there is a minor effect of alkyl chain length of QAS (such as, TMAB to TEAB) on methane hydrate inhibition, this observation is inline with some of the literature observations on the effect of alkyl chain length of ionic liquids on the phase equilibrium of methane hydrate system, which indicate that the shorter alkyl

Table 3. Enthalpy of Dissociation (ΔHd/(kJ·mol−1)) for Methane Hydrate in the Presence of Various QAS Aqueous Solutions no.

system

1 2 3 4 5 6 7

pure water TMAB TEAB TEAB TMAB TBAB TBAB

mass fractiona

ΔHd /(kJ·mol−1)a

0.05 0.05 0.10 0.10 0.05 0.10

53.9 59.6 54.1 59.3 65.9 177.4b 199.7c

remark this this this this this this this

work work work work work work work

a Expanded uncertainties U(mass fraction) = ± 0.0001; U(ΔHd ) = ±1.4 kJ·mol−1 (0.95 level of confidence). bCalculated from the phase equilibrium data of Sangwai and Oellrich.11 cCalculated from the phase equilibrium data of Arjmandi et al.10

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methane hydrate have also been predicted in the presence of QAS (TMAB/TEAB) aqueous solutions studied in the present work and also for various methane hydrate and salt/TBAB systems from the open literature.9,39 Two parameters, namely, k (for TMAB/TEAB) and k and y (for TBAB) are used to tune the thermodynamic phase equilibrium model. The k value is used to compute the activity of water in a particular salt, while the parameter y takes care of variation in vapor pressure in unfilled hydrate due to variations in the concentration of TBAB. 3.3.1. Model Development and Discussion. The details on the basic model equations which are available elsewhere4,38,40,41 are not reproduced here but are provided in the Supporting Information. This thermodynamic model is primarily based on the van der Waals and Platteeuw (vdWP) model40 which considers the equality of the fugacity of water in the hydrate phase and the corresponding liquid phase. In this work, the Peng−Robinson equation of states has been used to calculate vapor phase fugacity. Equations S13 and S22 (in the Supporting Information) are used for prediction of phase equilibrium conditions of the methane hydrate in the presence of TMAB/ TEAB and TBAB aqueous solutions. The structure of methane hydrate + TMAB/TEAB aqueous solutions is assumed as structure I as apparent from the ΔHd values shown in Table 3. The structure for TBAB hydrate is considered from literature.15 3.3.1.1. The Activity of Water in the Presence of Various Solutes. The activity of water (aw) in eqs S13 and S22 is a crucial tuning parameter for the prediction of phase equilibrium of methane hydrate + QAS aqueous solutions. The activity of pure water is 1 (for pure water) and reduces with a decrease in prevailing vapor pressure upon the addition of the solutes. The activity of water can be calculated from some known value of osmotic coefficient (φ) in the presence of various solutes.42,43 The activity of liquid water + QAS systems has been calculated as in eq 2. Equation 2 provides the relation between activity of water and osmotic coefficient φ, where v represents the number of ions and mi denotes the molality of the solute. Once the osmotic coefficient is identified for the particular molality, the activity for respective aqueous solution can be estimated. Unfortunately, the methods to estimate the osmotic coefficient at a particular molality of solute is very difficult. Consequently, to compute the activity, the exponential term in eq 2 has been expanded as a series in eq 3.44 p a w = v = exp( −0.018mivφ) pvw (2)

of TMAB and TEAB do not alter or distort the existing structure of pure methane hydrate (sI).1,34 For more clarity on structural differences, the values of the enthalpy of dissociation of hydrates for some gases are shown in Table S1 (see Supporting Information). For propane hydrate, ΔHd is equal to 129 kJ·mol−1 and forms structure sII. The ΔHd for TBAB hydrate is 177 and 199 kJ·mol−1 for 0.05 and 0.1 mf, respectively, which implies that methane hydrate + TBAB is a more stable hydrate system as compared to methane hydrate in TMAB and TEAB aqueous systems. There is always a structural change in hydrate when there is a significant increase in the value of ΔHd. Hence, based on the ΔHd values, lower alkyl chain length QASs (such as TMAB, and TEAB) present in an aqueous system does not affect the structure of methane hydrate system. 3.2.2. Electrical Conductivity Measurements. Ionic interactions may be responsible for inhibition of methane hydrate + (TMAB and TEAB) aqueous solutions. Electrical conductivity experiments are performed to investigate any ionic interactions which can be responsible for hydrate inhibition. An electrical conductivity meter (PC2700, Eutech instruments, Singapore) has been used for investigation. It has an electrical conductivity measuring range of 0.050 mS/cm to 500.0 mS/cm and can measure up to ±1% full-scale accuracy. The measured values of electrical conductivity of aqueous solutions of TMAB, TEAB, and TBAB at concentrations of 0.05 mf and 0.1 mf are reported in Table 4. It is observed that the shorter alkyl chain length of Table 4. Electrical Conductivity Values of Aqueous Solutions of Quaternary Ammonium Salt (This Work)a no

component

mass fractiona

electrical conductivity/(mS/cm)a

1

TMAB

2

TEAB

3

TBAB

0.05 0.10 0.05 0.10 0.05 0.10

25.21 44.17 18.31 29.57 8.68 13.41

Expanded uncertainties U(mass fraction) = ±0.0001; U(electrical conductivity) = ±0.01 mS/cm (0.95 level of confidence).

a

QAS displays higher electrical conductivity, and the order of electrical conductivity is TMAB > TEAB > TBAB. The conductivity increases with increase in concentration and follows the same order. The electrical conductivity measurement follows the similar trend as that of methane hydrate inhibition in the presence of TMAB and TEAB, while TBAB promotes the hydrate formation. This shows that the thermodynamic methane hydrate inhibition effectiveness of TMAB/TEAB is closely related to the electrical conductivity of the respective aqueous solution. The electrical conductivity measurements in ionic liquid aqueous solutions also show a similar kind of behavior. Ionic liquids with higher electrical conductivity generally show higher thermodynamic hydrate inhibition effects.36 It has also been observed from the study involving ionic liquids that the electrical conductivity decreases with increase in molecular weight, that is, due to increase in the alkyl chain length of the cation.37 3.3. Phase Equilibrium Model. A thermodynamic phase equilibrium model for the methane hydrate + TMAB/TEAB/ TBAB aqueous solutions has been presented here which is an extension to the model presented in our previous work and other literature.4,25,38 The phase equilibrium conditions of

a w = 1 − (0.018vφ)m i + −

(0.018vφ)3 m i 3 3′

(0.018vφ)2 m i 2 2′ (3)

If eq 4 is satisfied then the higher terms of eq 3 can be, therefore, simplified to eq 5.45 (0.018vφ) ≪ 1

(4)

a w ≅ 1 − (0.018vφ)m i

(5)

Further common electrolytes, for example NaCl and KCl have one anion and one cation, that is, v is 2. A careful evaluation on the osmotic coefficients of electrolytes suggest the agreement of eq 4. The maximum value of 0.018vφ in eq 4 is found to be 0.040 and 0.0354 for NaCl and KCl, respectively.45 In this case, E



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Table 5. Details of Various Model Parameters and AARD/P (%) for Prediction of Methane Hydrate Phase Equilibrium (This Work) in the Presence of Salts and QAS Aqueous Solutions tuned parameters electrolytes/ ILs

mass fraction

NaCla

0.05 0.0544 0.1083 0.11 0.05 0.0683 0.1341 0.05 0.1 0.05 0.05 0.1 0.0679 0.05 0.1 0.2 0.28 0.45

KCla

TMAB

TEAB

TBAB

a

molality (mol·kg solvent) 0.8556 0.9309 1.8532 1.8823 0.6707 0.9161 1.7988 0.3245 0.6491 0.3245 0.2379 0.4758 0.32309 0.1551 0.3102 0.6204 0.7755 1.3959

−1

of

activity of water

temp range/K

pressure range/ MPa

constant k

0.9678 0.9650 0.9302 0.9290 0.9750 0.9702 0.9415 0.985 0.985 0.971 0.986 0.976 0.983 0.996 0.991 0.984 0.978 0.966

277.5−283.6 277.09−284.2 274.7−280.60 279.16−288.3 276.3−283.2 275.49−284.1 275.09−280.91 282.4−277.78 281.48−278.08 287.8−282.64 282.58−279.28 282.18−277.18 287.67−282.65 281.75−288.45 284.25−290.35 286.05−291.55 287.15−292.35 286.25−291.25

5.0−9.6 4.84−10.57 4.92−9.57 7.51−23.88 4.31−8.89 4.02−10.32 5.02−9.67 7.6−4.77 7.3−5.01 13.31−7.66 7.42−5.53 7.39−4.55 14.05−7.64 1.56−7.042 1.013−6.198 0.797−5.522 0.94−5.234 0.708−4.126

0.0376 0.0376 0.0376 0.0376 0.0325 0.0325 0.0325 0.044 0.044 0.044 0.0504 0.0504 0.0504 0.0238 0.0238 0.0238 0.0238 0.0238

constant y

AARD/ P(%)

lit.

−11.580 −6.15 −3.127 −2.33 −1.483

−0.340 0.329 −0.365 0.896 −2.196 0.476 1.510 0.3652 3.24 −3.38 2.564 −2.538 1.445 0.1399 −3.48 1.757 −2.942 −2.588

Mohammadi et al.50 Cha et al.39 Cha et al.39 Mohammadi et al.50 Mohammadi et al.50 Cha et al.39 Cha et al.39 this work this work expt data20 this work this work expt data20 expt data9 expt data9 expt data9 expt data9 expt data9

Gupta et al.25

QAS has one anion and one cation, therefore, v is 2. The value of 0.018vφ for TBAB is found to be 0.019 for 0.47 molality.46 Hence, the value of 0.018vφ reasonably satisfies eq 4 for the QAS solutions used in this work. Therefore, eq 5 for QASs may be rewritten as in eq 6.45 Equation 6 can be applied satisfactorily to calculate the activity of the QAS in water up to mass fraction of 0.45 mf (as the experiment data are limited to 0.45 mf).

a w ≅ 1 − km i

where, P(expt) denotes the experimental equilibrium pressure, P(pred) represents the predicted pressure of methane hydrate, and N is the number of experimental phase equilibrium data. The k value is an important parameter in thermodynamic modeling of methane hydrate + QAS aqueous solutions and has different values at different concentrations of QAS. It is the parameter which needs to be tuned for TMAB/TEAB as a solute. Initially, to validate the procedure, the k value is obtained for a sample methane hydrate + KCl and methane hydrate + NaCl systems by applying regression analysis on the experimental phase equilibrium data on methane hydrate + (KCl and for NaCl) aqueous solutions.25,39 At least two experimental phase equilibrium data are required to precisely tune the value of k. The numerical value of the activity of the solution at a given concentration is adjusted so as to obtain a close fit with phase equilibrium experimental data using nonlinear regression. The process is repeated for other concentrations. Once we have the value of activities at two different concentrations (obtained from closely fitting phase equilibrium data) the value of k is obtained by linearly regressing the values of activities obtained (since the activity of solute varies linearly with molality for some definite concentration as discussed above). The k value can be further fine-tuned by the availability of more experimental data at other concentrations of the salts. The k value so obtained for both NaCl and KCl are 0.0376 and 0.0325 (also shown in Table 5) and match well with the k values reported in the literature, which are 0.03248 for KCl and 0.03710 for NaCl.25,45 Using the above method, the phase equilibrium conditions of methane hydrate + KCl aqueous solution at 0.05 mf, 0.0683 mf, and 0.13.41 mf have been predicted with AARD/P (%) of −2.196, 0.476, and −1.510, respectively (and are shown in Figure 4 and Table 5). Similarly, the phase equilibrium conditions of methane hydrate + NaCl aqueous solution at different mass fraction have been predicted as shown in Table 5. The method is then extended for methane hydrate + TMAB/ TEAB aqueous solutions of this work and the corresponding k

(6)

The slope k (=0.018vφ) (henceforth called as k value) in eq 6 is reliant on the number of dissociated ions and value of osmotic coefficient for a given QAS. In eq 6, the activity of an aqueous solution varies linearly for some range of molality. For NaCl and KCl, the maximum molality for which eq 6 is valid is 4.013 and 4.471, respectively.45 However, for QAS systems, it has been assumed that eq 6 is valid for all the concentrations used in this work. An additional tuning parameter y (eq S21 in Supporting Information) is required to predict the phase equilibrium of the methane hydrate + TBAB aqueous solution. Parameter y depends on variation in vapor pressure in unfilled hydrate due to changes in the concentration of TBAB which is not the case in the TMAB/TEAB systems. The approach used here is to tune the values of k and y to the experimental phase equilibrium data to find the activity for a particular aqueous solution in hydrate systems. This method escapes the number of several parameters that were involved in calculating the activity of water in the presence of various solutes.4,32,47−49 To appreciate our model predictions with that of actual experimental data, absolute average relative deviation [AARD/P (%)] is used and is defined as eq 7: AARD/P(%) =

100 N

⎡ P(pred) − P(expt) ⎤ ⎥ ⎢ ⎥⎦ P(expt) i=1 ⎣ N

∑⎢

(7) F



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Figure 4. Experimental and model predicted methane hydrate equilibrium pressure for various KCl concentrations. Experimental data from Cha et al.:39 0.05 mf (blue, ●); 0.1341 mf (black, ⧫); 0.0683 mf (red, ▲); and model prediction (, this work).

values and AARD/P (%) are reported in Table 5, respectively. Figures 5 and 6 (and also see Table 5) show that the predictions of the phase equilibrium model are in good agreement with the experimental phase equilibrium data of methane hydrate + TMAB/TEAB aqueous systems from this work and by Su and co-workers.20 We also have predicted the phase equilibrium of methane hydrate + TBAB aqueous solutions.9 The values of activity of water in the presence of TBAB have been obtained from osmotic coefficient data at different mole fractions from the literature.46 The osmotic coefficient TBAB varies linearly with the molality of TBAB up to 1.6 molalities. Hence, the k value can be calculated from eq 6. The values of k for TBAB have been calculated from osmotic coefficient data46 and further fine-tuned by experimental phase equilibrium data on the methane hydrate + TBAB system. The value of k was found to be 0.028 (constant for all concentrations of TBAB, see Table 5). Once the activity of water in the presence of TBAB is known, the parameter y reported in eq S21 is then tuned by nonlinear regression analysis so as to predict the phase equilibrium conditions of methane hydrate in the presence of TBAB aquesous solutions. The values parameter y at different mass fractions of TBAB have also been reported in Table 5. The experimental values and model predictions for methane hydrate + TBAB aqueous systems are shown in Figure 7. In addition, we also have found a relationship between y and the concentration of TBAB as shown in eq 8 which can be used to evaluate the parameter y at different concentrations (mf of TBAB) of interest. Figure S1 shows the variation of parameter y with TBAB mass fraction. The parameter y can be obtained from eq 8 at an intermediate mass fractions of TBAB to use in the phase equilibrium model of the methane hydrate + TBAB system [eqs S21 and S22 in the Supporting Information]: y = q1 + q2 x (8)

Figure 5. Experimental and model predicted methane hydrate equilibrium pressure for different concentrations of TMAB in an aqueous solution: (a) 0.05 mf (this work); (b) 0.1 mf (this work); (c) 0.05 mf, Su et al.;20 and model prediction (, this work).

temperatures by the model for the methane hydrates in the presence of QAS aqueous solutions are in good agreement with experimental data. Figure 8a displays a plot of predicted equilibrium pressures from the model vs experimental equilibrium pressures for 91 data points for methane hydrate in the presence of various QAS aqueous solutions. The results demonstrate that there exists a good linear relationship between predicted model and experimental equilibrium pressure conditions with R2 = 0.9917. Relative deviations between the predicted and experimental equilibrium pressure data with respect to the experimental equilibrium pressures for various methane hydrate + QAS systems is shown in Figure 8b which shows that 85% of the model predicted equilibrium pressures

where, q1 = 0.33639 and q2 = 0.56588 are the constants at different mass fractions of TBAB, and x is the mass fraction of TBAB. The experimental and model predictions of phase equilibrium of methane hydrate + (TMAB/TEAB and TBAB) aqueous solutions are shown in Figures 4 to 7 and are reported in Table 5. The predicted equilibrium pressures at various G



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Figure 7. Experimental and model predicted methane hydrate equilibrium pressure for different concentrations of TBAB in an aqueous solution. Experimental data from Sun and Sun:9 0.05 mf (red, ●); 0.1 mf (purple, ⧫); 0.2 mf (green, ▲); (0.28 mf (black, ×); 0.45 mf (blue, ) and model prediction (, this work).

Figure 6. Experimental and model predicted methane hydrate equilibrium pressure for different concentrations of TEAB in an aqueous solution: (a) 0.05 mf (this work); (b) 0.1 mf (this work); (c) 0.0679 mf, Su et al.20 and model prediction (, this work).

are lying within ±5% of relative deviation with the experimental values. Figure 8. (a) Linear relationship between equilibrium pressures from model prediction vs experimental equilibrium pressures; (b) relative deviations between the predicted and experimental equilibrium pressure data with respect to the experimental equilibrium pressures for various methane hydrate + QAS systems.

4. CONCLUSION In this work, the effect of QASs of the bromide family with increasing alkyl chain length, such as tetra-methyl, tetra-ethyl, and tetra-butyl ammonium bromide (TMAB, TEAB, and TBAB) at two different concentrations (0.05 and 0.1 mass fraction) in an aqueous solution on the H-L-V phase equilibrium of a methane hydrate system has been investigated. Phase equilibrium data in the equilibrium pressure range of 7.6−4.2 MPa and temperature range of 282.4−276.8 K have been reported. It has been observed that the shorter alkyl chain length QASs, such as TMAB and TEAB, have shown thermodynamic inhibition unlike TBAB, which indicated hydrate promotion. The observed results for the lower alkyl

chain length of QASs (TMAB and TEAB) at two different concentrations studied in this work show inhibition, which is consistent with the study reported by Su and co-workers.20 Enthalpy of hydrate dissociation in the presence of various QAS systems shows that TMAB and TEAB do not participate in hydrate structural transformation. The electrical conductivity of QAS solutions and their methane hydrate inhibition/ H



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clathrate hydrates of tetrabutyl ammonium bromide. J. Chem. Eng. Data 2007, 52, 2153−2158. (11) Sangwai, J. S.; Oellrich, L. Phase equilibrium of semiclathrate hydrates of methane in aqueous solutions of tetra-n-butyl ammonium bromide (TBAB) and TBAB-NaCl. Fluid Phase Equilib. 2014, 367, 95−102. (12) Kamata, Y.; Oyama, H.; Shimada, W.; Ebinuma, T.; Takeya, S.; Uchida, T.; Nagao, J.; Narita, H. Gas separation method using tetra-nbutyl ammonium bromide semi-clathrate hydrate. Jpn. J. Appl. Phys. 2004, 43, 362−365. (13) Shimada, W.; Ebinuma, T.; Oyama, H.; Kamata, Y.; Takeya, S.; Uchida, T.; Nagao, J.; Narita, H. Separation of gas molecule using tetra-n-butyl ammonium bromide semi-clathrate hydrate crystals. Jpn. J. Appl. Phys. 2003, 42, L129−L131. (14) Ma, Q. L.; Qi, J. L.; Chen, G. J.; Sun, C. Y. Modeling study on phase equilibria of semiclathrate hydrates of pure gases and gas mixtures in aqueous solutions of TBAB and TBAF. Fluid Phase Equilib. 2016, 430, 178−187. (15) Shimada, W.; Shiro, M.; Kondo, H.; Takeya, S.; Oyama, H.; Ebinuma, T.; Narita, H. Tetra-n-butylammonium bromide−water (1/ 38). Acta Crystallogr., Sect. C: Cryst. Struct. Commun. 2005, 61, 65−66. (16) Sloan, E. D. Fundamental principles and applications of natural gas hydrates. Nature 2003, 426, 353−363. (17) Aladko, L. S. Hydrate formation in the system tetraethylammonium bromide-water. Russ. J. Gen. Chem. 2012, 82, 1913− 1915. (18) Aladko, L. S. Formation of (CX H2x+1)4NBr·nH2O(X = 1−3) hydrate. Russ. J. Gen. Chem. 2014, 84, 1065−1068. (19) Nilsson, E. J.; Alfredsson, V.; Bowron, D. T.; Edler, K. J. A neutron scattering and modelling study of aqueous solutions of tetramethylammonium and tetrapropylammonium bromide. Phys. Chem. Chem. Phys. 2016, 18, 11193−11201. (20) Su, Y.; Bernardi, S.; Searles, D. J.; Wang, L. Effect of carbon chain length of organic salts on the thermodynamic stability of methane hydrate. J. Chem. Eng. Data 2016, 61, 1952−1960. (21) Sun, Q.; Guo, X.; Liu, A.; Liu, B.; Huo, Y.; Chen, G. Experimental study on the separation of CH4 and N2 via hydrate formation in TBAB solution. Ind. Eng. Chem. Res. 2010, 50, 2284− 2288. (22) Mohammadi, A. H.; Richon, D. Phase equilibria of semiclathrate hydrates of tetra- n -butylammonium bromide + hydrogen sulfide and tetra- n -butylammonium bromide + methane. J. Chem. Eng. Data 2010, 55, 982−984. (23) Deschamps, J.; Dalmazzone, D. Dissociation enthalpies and phase equilibrium for TBAB semi-clathrate hydrates of N2, CO2, N2 + CO2 and CH4 + CO2. J. Therm. Anal. Calorim. 2009, 98, 113−118. (24) Deschamps, J.; Dalmazzone, D. Hydrogen storage in semiclathrate hydrates of tetra-butyl ammonium chloride and tetra-butyl phosphonium bromide. J. Chem. Eng. Data 2010, 55, 3395−3399. (25) Gupta, P.; Sakthivel, S.; Sangwai, J. S. Effect of aromatic/ aliphatic based ionic liquids on the phase behavior of methane hydrates: Experiments and modeling. J. Chem. Thermodyn. 2018, 117, 9−20. (26) Mech, D.; Sangwai, J. S. Phase stability of hydrates of methane in tetrahydrofuran aqueous solution and the effect of salt. J. Chem. Eng. Data 2014, 59, 3932−3937. (27) Tohidi, B.; Burgass, R. W.; Danesh, A.; Ostergaard, K. K.; Todd, A. C. Improving the accuracy of gas hydrate dissociation point measurements. Ann. N. Y. Acad. Sci. 2000, 912, 924−931. (28) Mech, D.; Sangwai, J. S. Phase equilibrium of the methane hydrate system in the presence of mixed promoters (THF + TBAB) and the effect of inhibitors (NaCl, methanol, and ethylene glycol). J. Chem. Eng. Data 2016, 61, 3607−3617. (29) Gayet, P.; Dicharry, C.; Marion, G.; Graciaa, A.; Lachaise, J.; Nesterov, A. Experimental determination of methane hydrate dissociation curve up to 55 MPa by using a small amount of surfactant as hydrate promoter. Chem. Eng. Sci. 2005, 60, 5751−5758. (30) Chu, C. K.; Lin, S. T.; Chen, Y. P.; Chen, P. C.; Chen, L. J. Chain length effect of ionic liquid 1-alkyl-3-methylimidazolium

promotion effect are found to be closely related. In addition, a phase equilibrium model has been extended to predict the phase behavior of methane hydrate + (TMAB, TEAB, or TBAB) aqueous solutions. The absolute average deviation in equilibrium pressure (AARD/P (%)) predicted from the proposed model with the experimental equilibrium pressure data generated in this work and from various data sets from the literature has been found to lie within ±3.2%, indicating the robustness of the model. The model prediction results also demonstrate that there exists a good relationship between model predicted and experimental equilibrium pressures with R2 = 0.9917 and that the 85% of the model predicted equilibrium pressures are lying within ±5% of relative deviation with the experimental values.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b00976. Basic model equations used for prediction of phase equilibrium conditions of the methane hydrate in the presence of TMAB/TEAB and TBAB aqueous solutions (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] Tel.: +91-44-2257 4825. Fax: +91-44-2257 4802. ORCID

Jitendra S. Sangwai: 0000-0001-8931-0483 Notes

The authors declare no competing financial interest.

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Phase Equilibrium of Methane Hydrate in the Presence of Aqueous

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