Experimental Study and Thermodynamic Modeling of Methane

Article pubs.acs.org/jced

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

Experimental Study and Thermodynamic Modeling of Methane Hydrate Dissociation Conditions in the Simultaneous Presence of BMIM-BF4 and Ethanol in Aqueous Solution Homa Ghaedi,† Jafar Javanmardi,*,† Ali Rasoolzadeh,† and Amir H Mohammadi‡,§ †

Department of Chemical, Petroleum and Gas Engineering, Shiraz University of Technology, Shiraz, Iran Discipline of Chemical Engineering, School of Engineering, University of KwaZulu-Natal, Howard College Campus, King George V Avenue, Durban, 4041, South Africa § Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, Calgary, Alberta T2N 1N4, Canada ‡

ABSTRACT: Experimental and thermodynamic results for methane hydrate dissociation conditions in the simultaneous presence of ethanol and 1-butyl-3-methylimidazolium tetrafluoroborate (BMIM-BF4) ionic liquid (IL) in aqueous solution are presented. Three different aqueous solutions including solution 1 (0.0142 mole fraction of ethanol, 0.0060 mole fraction of BMIM-BF4), solution 2 (0.0348 mole fraction of ethanol, 0.0059 mole fraction of BMIM-BF4) and solution 3 (0.0549 mole fraction of ethanol, 0.0058 mole fraction of BMIM-BF4) were used. An isochoric pressure-search method was used to perform the measurements. The experimental pressure and temperature ranges are (3.18 to 8.32) MPa and (273.6 to 283.3) K, respectively. The thermodynamic inhibition effects of these solutions on methane hydrate dissociation were observed and solution 3 leads to the strongest inhibition effect. The average hydrate dissociation temperature reduction for methane hydrate in the presence of solutions 1, 2, and 3 are approximately 1.0, 2.2, and 3.7 K, respectively, in comparison with the pure water case. Furthermore, to predict methane hydrate dissociation conditions, a van der Waals-Platteeuw (vdW-P) type model was used. The activity of water in the liquid/aqueous phase is computed using the NRTL activity coefficient model and the fugacity of the gas phase is accounted using the Peng−Robinson equation of state (PR EoS). Results indicate that there is a good agreement between the experimental and modeled data.

1. INTRODUCTION Gas hydrates, or clathrate hydrates, pertain to the category of the inclusion compounds. The basis of gas hydrate formation is the holding of small gases and/or some volatile liquids having a proper dimension and shape (guest) in the empty cages made by the junction of water molecules (host). The existence of the van der Waals intermolecular force between the guest molecules inside the cage and water molecules on the cage wall, leads to the stability of the gas hydrate lattice. Among the several gas hydrate crystalline structures, three well-known structures namely structure I (sI), structure II (sII), and structure H (sH) have been studied.1−3 The appropriate conditions for gas hydrates to form, are the existence of water as a host molecule, some gases and/or some volatile liquids with suitable sizes as a guest molecules, low temperatures, and high pressures.4 The main drawback of gas hydrates is their formation in natural gas pipelines, which causes the blockage of the pipeline and consequently, the pressure drops incurring huge economic costs. Therefore, some actions must be taken to prevent the gas hydrate formation such as water removal, heating, pressure reduction, and applying the inhibitors. Applying gas hydrate inhibitors is one of the best and feasible methods for this purpose.1,5−7 © XXXX American Chemical Society

In the traditional classification, two types of gas hydrate inhibitors are used: thermodynamic hydrate inhibitors (THIs) and kinetic hydrate inhibitors (KHIs). THIs make the hydrate stability region smaller by shifting the hydrate−liquid−vapor/ gas equilibrium (HLVE) curve (or hydrate dissociation conditions) to high pressures and low temperatures. The primary members of this group are monoethylene glycol (MEG), methanol, ethanol, and NaCl.8−11 THIs are used in the petroleum industry extensively because they have a qualified inhibition effect on gas hydrate formation and they are not expensive, but despite having these advantages, they have some disadvantages such as they must be used at high concentrations to ensure that adequate contact with water is gained. Furthermore, due to the low density and high vapor pressure, they are volatile and a huge loss of inhibitors may occur. On the other hand in some places, the pressure and temperature conditions are extremely suitable for hydrate formation, therefore, injection of THIs even in large quantities may not result in hydrate prevention.12−14 KHIs typically have no Received: January 14, 2018 Accepted: April 4, 2018

A

DOI: 10.1021/acs.jced.8b00046 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Materials along with Their Properties Used in This Worka

a

material

supplier

density at 293.15 K (g·cm−3)

molar mass (g·mol−1)

purity

BMIM-BF4 ethanol methane

Merck Merck Air Products

1.18 0.79 0.000668

226.026 46.070 16.043

0.99b 0.99b 0.9995c

Deionized water was used in the experiments. bMass fraction. cMole fraction.

introduced tetra ethylammonium chloride (TEACl) as the most effective IL among all the experimented ILs.27 Tariq et al. reviewed the role of ILs on gas hydrate inhibition in the presence of THIs and KHIs.28 Long et al. measured the phase equilibria and dissociation enthalpies of methane hydrate in the imidazolium-based IL aqueous solutions.29 Rasoolzadeh et al. experimented the kinetic inhibition effects of three ILs on methane hydrate formation and found that the imidazoliumbased ILs have a more inhibition effect.30 Qureshi et al. studied the kinetic and thermodynamic effects of ILs in the presence of several synergents on gas hydrate inhibition.31 Tariq et al. investigated the inhibition effects of five ammonium-based ILs on methane hydrate formation.32 Khan et al. studied the effect of tetra methylammonium hydroxide (TMAOH) as a novel hydrate inhibitor on methane and CO2 hydrate.33 Khan et al. performed an experimental study on the thermodynamic inhibition effect of ammonium-based ILs on the CO2 hydrate phase boundary.34 Nashed et al. performed the experimental and modeling studies on the thermodynamic inhibition of ILs on methane hydrate.35 Because of the high potential and flexibility of ILs, their use as gas hydrate inhibitors can be suggested as a striking topic. To study any probable synergistic thermodynamic inhibition effect, we have extended our previous work on distinguishing the effect of BMIM-BF4 on methane hydrate dissociation conditions in the presence of ternary mixtures of water, BMIM-BF4 and an organic thermodynamic inhibitor namely ethanol. The reason for choosing ethanol was the lack of experimental data for methane hydrate dissociation conditions in the simultaneous presence of ethanol and IL. The effects of MEG and NaCl on IL solutions have been investigated previously.23 Hence, in this work, the experimental study on methane hydrate dissociation conditions in the simultaneous presence of ethanol and BMIM-BF4 aqueous solutions was conducted. The van der Waals− Platteeuw (vdW-P) model1,36 coupled with the Peng− Robinson (PR) EoS37 and nonrandom two-liquid (NRTL) activity coefficient model38 was applied to predict the hydrate dissociation conditions.

impact on the hydrate phase equilibrium conditions, they only delay the hydrate nucleation and growth rate causing more time for hydrates to form. KHIs are used in the concentration of about 0.01 mass fraction. Polyvinylpyrrolidone (PVP) is one of the most well-known members of this group.15 In the past decade, several investigations were conducted using new types of inhibitors which have more efficient performances in comparison with the classical inhibitors. They not only make the hydrate region smaller, but also delay the hydrate nucleation and growth. Owning these unique properties, this type of inhibitor is called dual-function hydrate inhibitor.16 It has been proven that some groups of ILs have dual-function inhibition effects. ILs are a new type of chemical compounds with unique characteristics, making them the best alternative for organic and inorganic solvents, and because of tunable properties, there has been a significant attraction for the use of ILs in chemical processes in the past decade. ILs normally have a large and asymmetrical cation and a small anion. This property of asymmetry prevents polymerization. Strong ionic interactions between the molecules of this class of materials result in a low saturation pressure, low freezing point, difficult ignition, and being thermally stable.17,18 Chen et al. observed that BMIM-BF4 can intensify the thermodynamic inhibition effect of carbon dioxide hydrate formation.19 Xiao and Adidharma investigated the performance of five imidazoliumbased ILs as a new class of inhibitors called dual-function inhibitors. This type of inhibitors, due to strong electrostatic charges and the potential to create a hydrogen bond with water molecules, not only moves the hydrate phase boundary, but also postpones the formation of methane hydrate by decreasing the hydrate nucleation and growth rate.20 Xiao et al. extended their previous study to six dialkylimidazolium halide ILs in a pressure range of (10.5 to 20.5) MPa. In a similar manner to the ILs studied in their previous work, these ILs made methane hydrate formation region smaller, and postponed the formation of methane hydrate by deceleration of hydrate nucleation.21 Li et al. verified the inhibition effect of five ILs on methane hydrate formation in the pressure range of (3 to 17) MPa and temperature range of (276.15 to 289.15) K.22 Richard and Adidharma experimented methane hydrate formation conditions in the presence of aqueous solutions containing up to 0.40 mass fractions of EMIM-Cl in the pressure range of (10 to 20) MPa.23 Macias-Perez et al. studied CO2 hydrate stability conditions in the presence of two ILs namely EMIM-Cl and BMIM-Cl.24 Partoon et al. assessed methane hydrate dissociation conditions in the presence of EMIM-Cl and [OH-C2MIM]-Cl with 0.001, 0.005, and 0.01 of mass fractions in the pressure range of (4 to 12) MPa.25 Zare et al. investigated methane hydrate dissociation conditions in the presence of some other ILs in the pressure range of (7.08 to 12.16) MPa and temperature range of (281.9 to 287.4) K, and thermodynamic inhibition effects were observed.26 Keshavarz et al. reported methane hydrate dissociation conditions in the presence of three ILs in the pressure and temperature ranges of (2.48 to 6.58) MPa and (272.1 to 280) K, respectively. They

2. EXPERIMENTAL SECTION 2.1. Material. The materials used in this work are reported in Table 1. BMIM-BF4 with a mass fraction of 0.99 was purchased from Merck KgaA, Germany. Ethanol with a mass fraction of 0.99 was also purchased from Merck KgaA, Germany. Both of ethanol and BMIM-BF4 were used without any purification. Methane gas with a mole fraction of 0.9995 was purchased from the Air Products Company, Iran. The deionized water was utilized to prepare aqueous solutions. The aqueous solutions were prepared on the basis of the gravimetric method by applying a digital A&D balance (HR-200) with the precision of ±0.0001 g. 2.2. Apparatus. The stainless steel (SS-316) equilibrium cell equipped with double visible windows and effective internal volume of 0.075 m3 was used in this work. The cell can bear a pressure up to 15 MPa. A magnetic stirrer is used to make B



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next step, the temperature was slowly decreased until a considerable pressure drop occurred in the recorded pressure data or the hydrates were observed visually. After the gas hydrate formed, the heating step was started. In the heating step, the temperature was raised at a rate of 0.1 K·h−1. After the hydrate crystals completely disappeared, the point at which a sudden variation in the ramp of the (P−T) curve occurred can be considered as the dissociation point. Throughout the experimental work, equilibrium temperature and pressure points were recorded by a data acquisition system.27 Figure 3 exhibits a typical P−T curve. It is clear that in Figure 3, a sharp change in the P−T slope is observed. This point is considered the equilibrium dissociation point.

sufficient agitation to reach equilibrium. Figure 1 presents an overview of the high-pressure vessel utilized in this work.

Figure 1. Overview of the equilibrium cell.

The cell is immersed in an ethanol cooling bath. Adjustment of the temperature is conducted by utilizing a circulator (TCS1), which has a capability of programming (Julabo FP-50). The cell pressure could be measured by an absolute pressure transformer with the uncertainty of 0.25% of total pressure. The cell temperature is measured by a PT-1000 thermometer with the maximum uncertainty of ±0.1 K. A data acquisition system is applied for accumulating the pressure and temperature data of the system. A schematic view of the experimental setup is exhibited in Figure 2. 2.3. Experimental Procedure. Methane hydrate dissociation conditions were measured by the constant volume pressure-search method.16,39 For each experiment, the specific aqueous solution was introduced into the cell. The excess gas was discharged with a vacuum pump to ensure the complete vent of any existing gases. Then, to achieve a desirable pressure, methane was injected into the cell (far enough away from the methane hydrate stability zone in the presence of deionized water) in which the hydrate undoubtedly will not form. In the

Figure 3. Cooling and heating pattern for a typical experiment.

3. THERMODYNAMIC MODEL For hydrate dissociation conditions modeling, various methods have been presented. These methods could be classified into two categories: (1) empirical and graphical methods and (2) statistical thermodynamics based models. The widely used and well-known statistical thermodynamic model is the van der

Figure 2. Schematic view of the experimental setup: PI, pressure transmitter; TT, temperature transmitter. C



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Waals−Platteeuw (vdW-P) model.1,36 The essential condition for gas hydrate phase equilibria is the equality of water chemical potential in all coexisting phases. Since in the temperature range of hydrate formation, the water saturation pressure is very low, therefore the quantity of water in the vapor/gas phase is negligible and the equilibrium condition is as follows:1,40 μwH (T , P) = μwL/I (T , P)

ΔC P′w = −38.12 + 0.141(T − T0)

The values of thermodynamic reference properties of structure I and structure II are presented in Table 2.41 Table 2. Thermodynamic Reference Properties for Both Structure I and Structure II Hydrates41

(1)

μHw

where stands for the chemical potential of water in the hydrate phase and μL/I w represents water chemical potential in the liquid/aqueous or ice phase. T and P are the temperature and the pressure, respectively. By considering the chemical potential of the empty hydrate lattice as a reference state, μβw, eq 1 can be presented in the following form:1,40 μwβ − μwH = μwβ − μwL/I

(3)

⎛ νm ln⎜⎜1 + ⎝

∑ m=1

RT0

Δμw0

=

RT0 +

∫0

−

∫T

T

0

P

Δhwβ ‐ L/I RT 2

i

⎠

(4)

RT0

−

∫T

T

0

no. of cavity

−

∑ m=1

Δhwβ ‐ L/I

Δνwβ ‐ L/I dP 0 RT RT 2 nc ⎛ ⎞ ⎜ νm ln⎜1 + ∑ Cmifi ⎟⎟ − ln(x wγw ) = 0 ⎝ ⎠ i=1 dT +

∫

∫T

(5)

1 ⎡⎛⎜ r a ⎞⎟ ⎢ 1− − ⎝ N⎣ R′ R′ ⎠

−N

δN =

(9)

(10)

−N ⎛ r a ⎞⎟ ⎤ ⎥ − ⎜1 + − ⎝ R′ R′ ⎠ ⎦

(12)

In eqs 9−12, k refers to Boltzmann’s constant, a indicates the molecular core radius, R′ is the cavity radius, w(r) is the potential function, ε is the minimum potential energy, σ* is the collision diameter, and Z is the coordination number. N is a constant that can be 4, 5, 10, or 11 and r is the guest distance from the cavity center. f i is the fugacity of the guest molecule in the vapor/gas phase which has been computed using the Peng−Robinson EoS.37 xw is the mole fraction of water in the liquid/aqueous phase, and γw is the water activity coefficient in the liquid/aqueous phase.

(6)

x w = 1 − xmethane − xethanol − xBMIM ‐ BF4

(13)

where xmethane is the mole fraction of methane is in the liquid/ aqueous phase, xethanol is the mole fraction of ethanol in the liquid/aqueous phase, and finally xBHIM‑BF4 is the mole fraction of BMIM-BF4 in the liquid/aqueous phase. The solubility of methane in water is calculated through Henry’s law:42

T

0

⎛ −w(r ) ⎞ 2 exp⎜ ⎟r d r ⎝ kT ⎠

(11)

P

ΔC P′w dT

R ′− a

⎡ σ *12 ⎛ a 11⎟⎞ σ *6 ⎛ a 5⎟⎞⎤ w(r ) = 2Zε⎢ 11 ⎜δ10 + δ − 5 ⎜δ 4 + δ ⎥ R′ ⎠ R′ r ⎝ R ′ ⎠⎦ ⎣ R′ r ⎝

In eq 6, Δμw0 is the chemical potential difference of water at reference conditions and Δvβ‑L/I is the molar volume difference w of water between the empty hydrate lattice and the liquid or ice phase, and both of them have a specific value for each structure.1,40 T0 refers to the reference temperature. Δhβ‑L/I is w the difference between an enthalpy of water in the empty hydrate lattice and in the liquid/ice phase which has a temperature dependency like the following form:1,40 Δhwβ‐ L/I = Δhw0 +

∫0

In eq 10, Γ(r) represents the Kihara potential function between the guest molecule and water molecule. For representation of the interaction between the guest molecule and all the water molecules on the hydrate cavity walls, eq 11 must be used.

dT

Δνwβ ‐ L/I dP − ln(x wγw ) RT

4π kT

⎡⎛ σ * ⎞12 ⎛ σ * ⎞6 ⎤ ⎟ ⎟ ⎥ Γ(r ) = 4ε⎢⎜ −⎜ ⎝ r − 2a ⎠ ⎦ ⎣⎝ r − 2a ⎠

The combination of eqs 3, 4, and 5 creates an important governing equation: Δμw0

882.80 −5202.2 5.0

Cmi(T ) =

where vm represents the number of m-type cavities, R stands for the universal gas constant, Cmi stands for the Langmuir constant of guest i in the m-type cavity and finally f i represents the guest fugacity in the vapor/gas phase. The right side of eq 3 was presented by Holder et al.40 as follows:40 Δμwβ ‐ L/I

1263.60 −4858.9 4.6

Cmi represents the Langmuir constant of the guest i in the mtype cavity which can be computed through a proper potential function such as the spherical core Kihara potential function:1

⎞

nc

∑ Cm fi ⎟⎟ i=1

structure II

Notation: Δμ0w, chemical potential difference of water at reference conditions; Δh0w, enthalpy difference of water in the empty hydrate lattice and the liquid/ice phase at reference conditions; Δvβ‑I w , molar volume difference of water in the empty hydrate lattice and liquid phase.

The left side of eq 3 can be derived from the statistical solution theory presented by vdW-P:1,36 No.of cavity

structure I

Δμ0w (J mol−1) Δh0w (J mol−1) 3 −1 Δvβ‑I w (cm mol )

1,40

Δμwβ ‐ H (T , P) = Δμwβ ‐ L/I (T , P)

Δμwβ− H = RT

parametera

a

(2)

Hence, eq 2 can be presented as follows:

(8)

(7)

Δh0w has a specific value for each structure and ΔC′Pw is the heat capacity difference of water which can be calculated from the following equation:1,40 D



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fmethane

xmethane =

PV̅ ∞ RT

( )

H exp

H (0) H (1) H (2) H (3) + + ln(T ) + T R RT R R

−ln(H ) =

(14)

4. RESULTS AND DISCUSSION Table 5 reports 35 experimental data on methane hydrate dissociation conditions in the presence of aqueous solutions

(15)

Table 5. Experimental Methane Hydrate Dissociation Conditions in the Presence of Different Aqueous Solutionsa

where f methane is the fugacity of methane in the vapor/gas phase, H is the methane Henry’s constant, V̅ ∞ is the partial molar volume of methane at infinite dilution in water which is set as a constant of 34.5 cm3.mol−1.42,43 P is the total pressure. H(0), H(1), H(2), and H(3) are constants for each component. Table 3 shows the model parameters for the methane hydrate system.

P/MPa

Table 3. Model Parametersa for Methane Hydrate System1,42,44 hydrate former

Tc (K)

methane

190.56

Pc (MPa)

a (Å)

σ* (Å)

ε/k (K)

4.599 0.0115 0.3834 Henry’s Constants

ω

3.1434

155.59

component

H(0)

H(1)

H(2)

H(3)

methane

−365.183

18106.700

49.7554

−0.000285

Notation: Tc, critical temperature; Pc, critical pressure; ω, acentric factor; a, molecular core radius; ε, minimum potential energy; σ*, collision diameter; k, Boltzmann’s constant. a

In this work, to calculate the water activity coefficient in the liquid/aqueous phase, the NRTL activity model38 was used, as mentioned earlier. For a solution of m components, the NRTL activity coefficient model is as follows: m

ln γi =

∑ j = 1 τjiGjixj m

∑l = 1 Glixl

m

+

∑ j=1

m ⎛ ∑r = 1 xrτrjGrj ⎞ ⎜ ⎟ τij − m m ∑l = 1 Gljxl ⎟⎠ ∑l = 1 Gljxl ⎜⎝

xjGij

(16)

τji =

Δgji (17)

RT

Gji = exp( −αjiτji)

(18)

αji = αij

(19)

T/K

Solution 1 0.0142 mol Fraction of Ethanol + 0.0060 mol Fraction of BMIM-BF4 3.18 274.5 3.72 275.8 4.26 276.8 4.85 278.2 5.53 279.6 5.97 280.3 6.21 280.5 6.32 280.6 6.45 281.1 6.85 281.6 7.16 281.8 8.29 283.3 8.32 283.3 Solution 2 0.0348 mol Fraction of Ethanol + 0.0059 mol Fraction of BMIM-BF4 3.81 275.2 4.04 275.7 4.28 276.1 4.47 276.6 5.08 277. 7 5.75 278.6 6.34 279.7 6.77 280.1 6.80 280.2 7.61 281.3 7.61 281.4 Solution 3 0.0549 mol Fraction of Ethanol + 0.0058 mol Fraction of BMIM-BF4 3.91 273.6 4.25 274.3 4.71 275.7 4.73 275.8 5.19 276.2 5.80 277.4 6.23 278.4 6.97 278.9 7.47 279.9 7.98 280.3 8.00 280.7

In eqs 17 and 18, Δgji is the binary energy parameter and αji is the nonrandomness factor. Table 4 presents the NRTL parameters for the water−ethanol−BMIM-BF4 system.45

The expanded uncertainty Uc is Uc(T) = ±0.1 K, Uc(w) = ±0.01, Uc(P) = ±0.01 MPa (0.95 level of confidence).

a

Table 4. NRTL Parameters Used in This Work (Water (1), Ethanol (2), BMIM-BF4 (3))45 Δg13 Δg31 Δg23 Δg32 Δg12 Δg21 α13 α23 α12 a

(J (J (J (J (J (J

mol−1) mol−1) mol−1) mol−1) mol−1) mol−1)

5406.9 −3523.1 8301.9 −2799.6 3698.8 + 4.2758Ta −2216.0 + 6.7055Ta 0.3 0.3 0.4

with different concentrations containing, 13 experimental data for solution 1, 11 experimental data for solution 2, and 11 experimental data for solution 3. Initially, we compared the thermodynamic model results and some selected experimental data for methane hydrate dissociation conditions in the presence of pure water.27,46−48 Also, in our previous work, the experimental method was already verified by generating few data points for a known system of methane + water and successful comparison with literature data.49 Figure 4 presents the comparison between the

T is in K. E



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BMIM-BF4 and water in all three solutions were 1.39 g and 18.05 g, respectively. But the amount of ethanol was changed in each solution. The amounts of ethanol in solutions 1, 2, and 3 were 0.67, 1.67, and 2.69 g, respectively. This means that the amount of IL was fixed and the amounts of ethanol were increased to investigate the effect of ethanol addition in BMIMBF4 aqueous solution on methane hydrate formation inhibition. At constant pressure, solutions 1, 2, and 3 decrease the average methane hydrate dissociation temperatures about 1.0, 2.2, and 3.7 K, respectively, whereas 0.10 mass fraction of ethylene glycol as a common thermodynamic inhibitor shifts the methane hydrate dissociation temperature about 2−2.5 K.1 Thus, the combination of ethanol and BMIM-BF4 especially at a considerable mole fraction of ethanol (solutions 2 and 3), has a strong inhibition effect because of the presence of OH bonds in higher values and coverage of more water molecules. It is clear from Figure 5 that the horizontal distance between the hydrate equilibrium curves for different solutions and pure water increases as pressure increases, thus the inhibition effect of solutions is more sensible at high pressures. Table 6 presents

experimental and modeling results for methane hydrate dissociation conditions in the presence of pure water.

Figure 4. Comparison between the modeling results and experimental data27,46−49 for methane hydrate dissociation conditions in the presence of pure water.

Table 6. Methane Hydrate Dissociation Temperature Depressions (ΔTave) in the Presence of Different Aqueous Solutions

The average absolute deviation, AAD, of this system is 0.1 K. n

AAD =

∑i = 1 |(Tiexp − Tical)| n

thermodynamic inhibitor

(20)

0.0142 0.0348 0.0549 0.0142 0.0348 0.0549 0.0060 0.0059 0.0058

As can be observed, the model can predict the methane hydrate dissociation conditions with a good accuracy. The thermodynamic inhibition strength of the three solutions and shifting the stability zone of methane hydrate is shown in Figure 5. For comparison, the predicted methane

a

mol mol mol mol mol mol mol mol mol

fraction fraction fraction fraction fraction fraction fraction fraction fraction

of of of of of of of of of

ethanol, 0.0060 mol fraction of BMIM-BF4 ethanol, 0.0059 mol fraction of BMIM-BF4 ethanol, 0.0058 mol fraction of BMIM-BF4 ethanol ethanol ethanol BMIM-BF4 BMIM-BF4 BMIM-BF4

Calculated as ΔTave =

ΔTavea 1.0 2.2 3.7 1.0 2.2 3.2 0.4 0.4 0.4

∑in= 1(Tipure − Tiinhibitor) n

the average dissociation temperature depressions for various aqueous solutions studied in this work. Moreover, for better comparison, these depressions for individual ethanol and BMIM-BF4 in aqueous solutions with the same concentration as the studied solutions have also been given. As shown in this table, in the simultaneous presence of these two inhibitors, the depression is slightly lower than the sum of depressions for each single inhibitor. However, BMIM-BF4 can act as a dual function inhibitor and can increase the induction time. It should be noted that in this table, for the case of ethanol + IL, the experimental hydrate dissociation temperatures were used to calculate the depressions and for the individual presence of ethanol and IL in aqueous solutions, because of the lack of experimental data in these concentrations, the thermodynamic model predictions were used. It can be concluded that the stronger inhibition effect of solution 3 in comparison with 0.0549 mole fraction of ethanol in solution is due to the existence of BMIM-BF4 in solution 3. BMIM-BF4 has a long-chain cation and a small anion, which results in owning an asymmetric structure that has a strong electrostatic charge. This kind of force decreases the water activity which leads to a greater inhibition effect. The higher negative values for water activity means a greater inhibition effect. It is obvious, however, that ethanol has a stronger inhibition effect on methane hydrate in comparison with

Figure 5. Comparison between the predicted and experimental data of methane hydrate dissociation conditions in the presence of different aqueous solutions.

hydrate dissociation conditions are also presented. As can be observed in Figure 5, the thermodynamic model used in this study, predicts hydrate stability zone for the ternary mixture of water + ethanol + BMIM-BF4 with a good accuracy. The AAD for the experimental and modeling results of methane hydrate dissociation temperatures for the three solutions used in this work are 0.3, 0.4, and 0.3 K, respectively. It is worth mentioning that no optimizing parameter was used for model predictions. In this work, three different aqueous solutions of BMIM-BF4 and ethanol were used, as mentioned earlier. The amounts of F



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Δμβ‑L/I w

BMIM-BF4, and ethanol can play a synergist compound role for BMIM-BF4 for methane hydrate inhibition. Finally, it should be pointed out that we have assumed that the studied ionic liquid and ethanol do not take part in methane hydrate structure. However, this assumption requires further investigation using a suitable physical technique (e.g., Raman Spectroscopy, X-ray, NMR, etc.).

Cmi fi R T vw

5. CONCLUSION The experimental study and thermodynamic modeling of methane hydrate dissociation conditions in the simultaneous presence of (ethanol + BMIM-BF4) in aqueous solutions have been undertaken. The experimental dissociation pressure and temperature ranges are (3.18 to 8.32) MPa and (273.6 to 283.3) K, respectively. An isochoric pressure−search method was used to undertake the measurements. The combination of vdW-P and NRTL activity coefficient models was employed to calculate the water chemical potential difference between the liquid/aqueous phase and empty hydrate lattice. The Peng− Robinson EoS was used to calculate the fugacity of methane in the gas phase. To calculate the solubility of methane in the water, the Henry’s law was applied. We first compared the thermodynamic model results with some selected experimental data on methane hydrate dissociation conditions in the presence of pure water. A good agreement between the experimental and predicted data is observed. The experimental results for the three different solutions of simultaneous ethanol and BMIM-BF4 show that this combination of inhibitors contributes to a great inhibition effect. Furthermore, it was concluded that ethanol can play a role of the stronger inhibitor in comparison with BMIM-BF4. This is mainly because the presence of OH bonds in ethanol molecules, which hydrogen bond with water molecules, can lead to coverage of much more water molecules in comparison with BMIM-BF4. That is to say the simultaneous presence of ethanol and BMIM-BF4 in aqueous solution results in a greater inhibition effect on methane hydrate than each one in pure water and with a similar concentration.

■

Δμ0w T0 Δhβ‑I/α w Δvβ‑I/α w Δh0w xw γw xmethane xethanol xBHIM‑BF4 ΔC′PW k a R′ Z σ* ε f Methane H V̅ ∞

AUTHOR INFORMATION

Corresponding Author

P γi τji Δgji αji

*E-mail: [email protected]. Tel.: +98-713-7354520. ORCID

Jafar Javanmardi: 0000-0002-4146-1490 Funding

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The authors express their gratitude to Shiraz University of Technology for supporting this research. Notes

chemical potential difference of water between the empty hydrate structure and the liquid/ice phase, (J mol−1) Langmiur constant of guest i in the cavity of type m, (MPa−1) fugacity of the guest molecule in the vapor/gas phase, (MPa) universal gas constant, (J mol−1 K−1) absolute temperature, (K) number of “m” type cavities per water molecule in the hydrate structure chemical potential difference of water at reference conditions in the liquid/aqueous phase and the empty hypothetical hydrate lattice, (J mol−1) reference temperature, (K) molar enthalpy difference of water in the empty hydrate structure and the liquid/ice phase, (J mol−1) molar volume difference of water in the empty hydrate structure and the liquid/ice phase, (cm3.mol−1) molar enthalpy difference of water in the empty hydrate structure and the liquid/ice phase at water freezing point, (J mol−1) mole fraction of water in the liquid/aqueous phase water activity coefficient in the liquid/aqueous phase mole fraction of methane in the liquid/aqueous phase mole fraction of ethanol in the liquid/aqueous phase mole fraction of BMIM-BF4 in the liquid/aqueous phase constant pressure specific heat capacity difference, (J mol−1.K−1) Boltzmann’s constant, (J.K−1) molecular hard core radius, (Å) average cavity radius, (Å) coordination number collision diameter, (Å) minimum potential energy, (J) Fugacity of methane in the gas phase methane Henry’s constant partial molar volume of methane at infinite dilution in water total pressure activity coefficient of component i NRTL binary parameter binary energy parameter nonrandomness factor

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The authors declare no competing financial interest.

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NOMENCLATURE chemical potential of water in the hydrate phase, (J mol−1) I/α μw chemical potential of water in the liquid/ice phase, (J mol−1) β chemical potential of water in the empty hydrate μw lattice, (J mol−1) β‑H Δμw chemical potential difference of water between the empty hydrate structure and the hydrate phase, (J mol−1) μHw

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Experimental Study and Thermodynamic Modeling of Methane

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