Prediction of Phase Equilibrium of Methane Hydrates in the Presence

Article pubs.acs.org/IECR

Prediction of Phase Equilibrium of Methane Hydrates in the Presence of Ionic Liquids Huai-Ying Chin,† Bong-Seop Lee,† Yan-Ping Chen,† Po-Chun Chen,‡ Shiang-Tai Lin,*,† and Li-Jen Chen*,† †

Department of Chemical Engineering, National Taiwan University, Taipei 10617, Taiwan Central Geological Survey, P.O. BOX 968, New Taipei City 235, Taiwan

‡

S Supporting Information *

ABSTRACT: In this work, a predictive method is applied to determine the vapor−liquid-hydrate three-phase equilibrium condition of methane hydrate in the presence of ionic liquids and other additives. The Peng−Robinson−Stryjek−Vera Equation of State (PRSV EOS) incorporated with the COSMO-SAC activity coefficient model through the first order modified Huron− Vidal (MHV1) mixing rule is used to evaluate the fugacities of vapor and liquid phases. A modified van der Waals and Platteeuw model is applied to describe the hydrate phase. The absolute average relative deviation in predicted temperature (AARD-T) is 0.31% (165 data points, temperature ranging from 273.6 to 291.59 K, and pressure ranging from 1.01 to 20.77 MPa). The method is further used to screen for the most effective thermodynamic inhibitors from a total of 1722 ionic liquids and 574 electrolytes (combined from 56 cations and 41 anions). The valence number of ionic species is found to be the primary factor of inhibition capability, with the higher valence leading to stronger inhibition effects. The molecular volume of ionic liquid is of secondary importance, with the smaller size resulting in stronger inhibition effects.

1. INTRODUCTION Gas hydrates are nonstoichiometric crystalline solids of water and gas molecules. Depending on the size, the gas molecules may be encapsulated in the cavities existing in one of the three types of frameworks: structure I (sI), II (sII), and H (sH).1 Methane hydrates have been attracting much attention because of their abundance in nature2 and the potential of serving as a source of energy.3 Gas hydrates may also be used as a media for sequestration of greenhouse gases, such as CO2.4,5 The addition of inhibitors, thermal and pressure stimulation, and the combination of these methods are the primary methods for gas hydrate recovery.6−9 Inhibitors are often introduced in the pipelines of oil recovery and transportation processes in order to prevent blockage by the formation of gas hydrates.10−12 The presence of inhibitors in the system shifts the three-phase-coexisting condition to a lower temperature (or higher pressure), and thus prevents the formation of gas hydrates. Organic solvents (e.g., alcohols) and saline solutions are considered as good inhibitors for gas hydrate formation. Maekawa, Mohammadi et al., and Haghighi et al.13−16 established the data of organic solvent inhibitors for methane, natural gas, propane, and carbon dioxide gas hydrate systems. Mohammadi et al.17,18 used an isochoric pressure-search method to generate the experimental data of electrolytes added in different kinds of gas hydrate. Considering cost and effectiveness, methanol has been the most widely used thermodynamic inhibitor for gas hydrates.10,12,16,19−21 In 2009, Xiao and Adidharma22 discovered a new type of inhibitors for gas hydrates, the ionic liquids (ILs). They found that ILs not only reduce the dissociation temperature of gas hydrates (thermodynamic inhibitor) but also prolong the time for their formations (kinetic inhibitor).22,23 They concluded © 2013 American Chemical Society

that ILs with a shorter alkyl chain substituent and higher electrical conductivity exhibit better inhibition effects. ILs have been regarded as green solvents for chemical processes because they are nonflammable, nonvolatile, and thermally stable.24 However, their direct use in the natural environment may still be of concern. Some ILs are environmentally benign and can be decomposed in wastewater treatments, either through biodegradation25,26 or electrochemical treatment.26 Deng et al.25 discovered that ILs with the presence of an ester group in the side chain are more easily biodegraded. There is a strong connection between the molecular structure of ILs and their functions as an inhibitor for gas hydrates and their environmental impact when used in the recovery. However, due to the structure diversity and the nearly unlimited combinations from cations and anions, the screen for candidate ILs could be a daunting task. In this work, we examine the prediction of the inhibition effects of ILs on the dissociation condition of gas hydrates based on the molecular structure of ILs. The Peng−Robinson−Stryjek−Vera (PRSV) EOS27 combined with the predictive COSMO-SAC activity coefficient model28 through the first order modified Huron− Vidal (MHV1) mixing rule29 is used for the fluid phase, and the van der Waals−Platteeuw model30 is used for the hydrate phase. The advantage of this approach is that no parameter fitting is needed for the ILs. The method is first validated using the rather scarce experimental data involving ILs. The effect of Received: Revised: Accepted: Published: 16985

August 18, 2013 October 30, 2013 October 31, 2013 October 31, 2013 dx.doi.org/10.1021/ie4027023 | Ind. Eng. Chem. Res. 2013, 52, 16985−16992

Industrial & Engineering Chemistry Research

Article

range, charge−charge interactions (the Pitzer−Debye−Huckel model) and the short-range, surface-contact interactions.

ILs on the equilibrium condition of gas hydrates is then explored based on the analysis of a large set of ILs.

ln γi = ln γi COSMOSAC + ln γi PDH

2. THEORY The equality of the fugacity of water in all phases (i.e., vapor, liquid, and hydrate phase) is used to determine the three-phasecoexisting phase equilibrium (H−Lw−V) at fixed temperature T and pressure P f wV (T , P , yi ) = f wL (T , P , xi) = f wH (T , P , yi )

γiCOSMOSAC

where and represent contributions from shortrange and long-range interactions, respectively. The short-range interactions include surface segment interactions from electrostatic (non-hydrogen bonding), hydrogen bonding, ionic, and ionic group, and size and shape effects

(1)

nhb,hb, ion,iongrp

where yi and xi are the mole fractions in the vapor and liquid phases, respectively; the superscripts V, L, and H denote for the vapor, liquid, and solid hydrate phase, respectively. The way to determine the water fugacity in each phase is introduced as follows. 2.1. Fugacity in the Fluid Phase. The Peng−Robinson− Stryjek−Vera equation of state (PRSV EOS), modified from the Peng−Robinson equation of state (PR EOS), is used in this study.27,31 P=

RT a − 2 ̲ V̲ − b V + 2bV̲ − b2

s

(3)

b = 0.077796

RTc Pc

(4)

κ = κ0 + κ1(1 + TR 0.5)(0.7 − TR )

−

κ0 = 0.378893 + 1.4897153ω − 0.17131848ω 2

where ω is the acentric factor. The parameters κ1 for each component in this study are taken from Stryjek and Vera.27,31 Note that κ1 is an adjustable characteristic parameter for each component in the PRSV EOS in order to improve the description of vapor pressure over the original PR EOS. For mixture calculations, a mixing rule is necessary to determine the composition dependence of am and bm in the PRSV EOS. In this work, the first order modified Huron−Vidal (MHV1) mixing rule29 is used

∑ xi ln i

bm ⎤ ⎥ bi ⎥⎦

ln γi

(7)

∑ xibi i

θ z qi ln i + li 2 ϕi

∑ xjlj (10)

j

∑ pjt (σnt )Γ sj(σnt ) σn

(11)

where subscript j may be solution S or a pure species i. ΔW(σm, σn) is the segment exchange energy representing the interaction between two segments of charge density σm and σn. The complete description of ΔW(σm, σn) between different types of segments can be found in Hsieh and Lin.32 On the other hand, the Pitzer−Debye−Hückel model33 is applied to cover the long interaction.

c

bm =

xi

+

⎫ ⎡ −ΔW (σ s , σ t ) ⎤⎪ ⎪ m n ⎥⎬ exp⎢ RT ⎣ ⎦⎪ ⎪ ⎭

(6)

c

xi

⎧ nhb,hb, ⎪ ion,iongrp ⎪ s s ln Γ j(σm) = −ln⎨ ∑ ⎪ t ⎪ ⎩

where Tc and Pc are the critical temperature and pressure of pure fluid and the reduced temperature TR = T/Tc.

c ⎡ Gex ⎛ a ⎞ 1 am = bmRT ∑ xi⎜ i ⎟ + bmRT ⎢ + ⎢⎣ RT q1 ⎝ buRT ⎠ i

ϕi

ϕi

where ni = Ai/aeff is the number of surface segments of species i, Ai is the surface area, and aeff is the effective segment area, the coordination number z is taken to be 10, and ϕi = xiri/∑jxjrj and θi = xiqi/∑jxjqj are the volume and surface area fractions (ri and q i are the normalized volume and surface area, respectively). The σ-profile pis(σm) is the probability of finding a segment of screening charge density σm of species i. The superscript s indicates one of the four kinds of surfaces: none hydrogen bonding (nhb), hydrogen bondings (hb), atomic ions (ion), and polyatomic ions (or ion groups, iongrp). Ionic liquids are considered as ionic groups. Γj(σm) is the activity coefficient of a single segment m with a charge density σm and is determined from

(5)

+ 0.0196554ω3

σm

− ln Γ is(σms)] + ln

where P, T, V, and R represent the pressure, temperature, molar volume, and gas constant, respectively. Both the energy parameter a and the volume parameter b are species-dependent and determined from critical properties as R2Tc 2 [1 + κ(1 − TR 0.5)]2 Pc

∑ ∑ pis (σms)[ln Γ Ss (σms)

ln γiCOSMOSAC = ni

(2)

a = 0.457235

(9)

γiPDH

PDH

⎛ 1000 ⎞1/2 ⎡⎛ 2zi 2 ⎞ ⎟ ln(1 + ρIx1/2) = −⎜ ⎟ Aϕ⎢⎜ ⎢⎣⎝ ρ ⎠ ⎝ Ms ⎠ ⎛ z 2I 1/2 − 2I 3/2 ⎞⎤ x ⎟⎟⎥ + ⎜⎜ i x 1/2 ⎝ 1 + ρIx ⎠⎥⎦

(8)

where q1 is fixed at −0.53 and the excess Gibbs free energy Gex is determined from a predictive liquid model, the COSMOSAC activity coefficient model.28,32 In this model, the activity coefficient is calculated with considerations of both the long-

(12)

where Ms is the average molecular weight of solvent, zi is the net charge of ion i, Ix is the ionic strength, and Aφ is the Debye−Hückel constant as 16986

dx.doi.org/10.1021/ie4027023 | Ind. Eng. Chem. Res. 2013, 52, 16985−16992

Industrial & Engineering Chemistry Research Ix =

1 2

∑ xizi 2

Article

Cml =

(13)

i

2 3/2 1/2 1 ⎛ 2πNAdS ⎞ ⎛ Q e ⎞ ⎟ ⎟ ⎜⎜ Aϕ = ⎜ 3 ⎝ 1000 ⎠ ⎝ εSkT ⎟⎠

Vml(P) = (14)

fi (T , P , x̲ ) xiP

=

1 ⎛ ∂Nbm ⎞ ⎜ ⎟ bm ⎝ ∂Ni ⎠

(Z − 1)

2 )bm ⎤ ⎥ 2 )bm ⎦

m

(15)

∑ θml)) l

(16)

⎛ P β ⎞ ⎜ ∫Pwsat Vw (T , P) dP ⎟ sat sat β f w (T , P) = Pw ϕw (T ) exp⎜ ⎟ RT ⎜ ⎟ ⎝ ⎠

(17)

where f βw is the empty hydrate fugacity, νm is the number of cages of type m per water molecule in the hydrate lattice, ϕsat w is the fugacity coefficient at saturated condition, Psat is the w saturated vapor pressure, and Vβw is the molar volume of water at empty hydrate. A unit cell of structure I hydrate includes 2 small (512) cages and 6 large (51262) cages for, in total, 46 water molecules, and a unit cell of structure II hydrate includes 16 small (512) cages and 8 large (51264) cages for, in total, 136 water molecules. Therefore, νm is 2/46 for the small cage in structure I, 6/46 for the large cage in structure I, 16/136 for the small cage in structure II, and 8/136 for the large cage in structure II. The occupancy, θml, of guest gas l in cage type m is calculated by Cmlf l̅ (T , P , yl ) V

1 + ∑l Cmlf l̅ (T , P , yl )

structure type

cavity type

sI

512 51262

Aml × 106 Bml × 106 2.786 0.688

0.720 49979

V0 × 103 (Å3)

εml/k (K)

44.592 501.136

2548.81 2548.81

3. COMPUTATIONAL DETAILS To determine the three-phase-coexisting equilibrium condition, the fugacity of water in each phase has to be calculated. At a given temperature and feed composition of additives and guest molecules, the isothermal flash calculation37 provides the pressure and composition of both the liquid and the vapor phases. The fugacities of water in fluid phases can be determined from eq 15. Furthermore, the hydrate phase water fugacity can be determined through the vdW-P model eq 16. If the hydrate phase fugacity is equal to that in the fluid phase, the equilibrium condition is found. Otherwise, a new pressure is estimated from the vdW-P model and the calculation is repeated until equality of fugacity in three-phase is achieved. It is noteworthy that the ways to determine the water fugacity in each phase are different. Recognizing the fact that ILs are nonvolatile, we assume that the ILs do not present in

V

θml =

(21)

The proposed pressure-dependent Langmuir adsorption constant is designed to produce a reduced free volume available to the encapsulated gas molecules at low and moderate pressures. This approach has been shown to be capable of describing various types of phase behavior of pure guest hydrate systems: vapor−ice−hydrate, vapor−liquid−hydrate, and liquid−liquid−hydrate equilibrium.35 Furthermore, the retrograde behavior observed in CH4, CO2, C3H8, and i-C4H10 pure gas hydrate systems can all be successfully described by the reduction of free volume at high pressures.35 In this work, we apply this pressure-dependent vdW-P model with the pressure function f ml(P), eq 21, to the systems of gas hydrate in the presence of ionic liquids as thermodynamic inhibitors. The advantage of this approach is that the reduction function of the free volume f ml, eq 21, is guest-independent (see Table 1) under low and moderate pressures (200 MPa).35 In other words, parameters Aml and Bml are independent of guest l, or Aml = Am and Bml = Bm. Consequently, this proposed model is fully predictive (no adjustable parameters) for all types of sI clathrate hydrates. In other words, the proposed model can be extended to predict the phase equilibrium of hydrate systems in the presence of ionic liquids without any additional adjustable parameters.

2.2. Water Fugacity in the Hydrate Phase. The van der Waals−Platteeuw model30 is the most widely used method for calculating water fugacity in the hydrate phase. In 2000, Klauda and Sandler34 rewrote the model in terms of the fugacity of water. f wH (T , P , yi ) = f wβ (T , P) exp(∑ νm ln(1 −

(20)

Table 1. Parameters Used for the van der Waals−Platteeuw Model (eq 21)35

⎡ 2 ⎛ Pbm ⎞ am ⎢⎛ 1 ∂N am ⎞ ⎟+ ⎜ ⎟ − ln⎜Z − ⎝ RT ⎠ 2 2 bmRT ⎢⎢⎝ Nam ∂Ni ⎠ T , Nj ≠ i ⎣ ⎤ ⎥ ⎡ V̲ + (1 − ⎥ ln⎢⎣ V̲ + (1 + T , Nj ≠ i ⎥ ⎦

0 V ml fml (P)

where Vml is the free volume of guest gas l in cage type m, εml is the square-well potential energy36 between guest gas l and host (water) molecules, the reduced pressure Δ = P/Pc and Pc is the critical pressure of water. The maximum free volume V0ml and the square-well potential energy εml are listed in Table 1.

T , Nj ≠ i

1 ⎛ ∂Nbm ⎞ − ⎜ ⎟ bm ⎝ ∂Ni ⎠

(19)

fml (P) = 1 + A ml Δ + Bml Δ2

where NA is the Avogadro constant, dS is the density of solvent, Qe = 1.6021892 × 10−19 C, k is the Boltzmann constant, and εS is the average dielectric constant of solvent. The fugacity expression from PRSV EOS for a species in a mixture can be given as follows ln

⎛ε ⎞ 4π Vml exp⎜ ml ⎟ ⎝ kT ⎠ kT

(18)

where Cml is the Langmuir adsorption constant of guest gas l in cage type m, fVl̅ is the fugacity of guest gas l in the vapor phase, and y1 is the mole fraction. In 2012, Hsieh et al.35 proposed the pressure-dependent Langmuir adsorption constant Cml as the following 16987



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Table 2. Prediction Accuracy of the Dissociation Conditions of Methane Hydrates upon of Addition Ionic Liquids and Other Inhibitors additive type MMIM-I EMIM-I EMIM-Br EMIM-Cl EMIM-EtSO4 EMIM-HSO4 EMIM-Cl + EMIM-Br EMIM-Cl + NaCl EMIM-Cl + EG PMIM-I BMIM-MeSO4 BMIM-BF4 BMIM-I BMIM-Br BMIM-Cl OHC2MIM-Cl OHC2MIM-BF4

IUPAC name 1,3-dimethylimidazolium iodide 1-ethyl-3-methylimidazolium iodide 1-ethyl-3-methylimidazolium bromide 1-ethyl-3-methylimidazolium chloride 1-ethyl-3-methylimidazolium ethylsulfate 1-ethyl-3-methylimidazolium bisulfate

1-propyl-3-methylimidazolium iodide 1-butyl-3-methylimidazolium methylsulfate 1-butyl-3-methylimidazolium tetrafluoroborate 1-butyl-3-methylimidazolium iodide 1-butyl-3-methylimidazolium bromide 1-butyl-3-methylimidazolium chloride 1-(2-hydroxyethyl)-3-methylimidazolium chloride 1-(2-hydroxyethyl)-3-methylimidazolium tetrafluoroborate

overall

data pts.

references

concentration of ionic liquid (wt %)

T range (K)

P range (MPa)

AARD-T (%)

5 5 6 50 9 5 3

39 39 23, 40 40, 42 41 41 40

10 10 10- 20 0.1- 40 8.0−10.0 10 20

276.68−288.0 276.72−288.04 284.7−290.81 273.6−291.4 284.6−287.4 281.9−287.2 281.9−287.2

4−14.29 3.99−14.12 1.01−2.01 3.88−20.77 8.67−11.65 7.07−11.95 9.7−19.8

0.178 0.153 0.556 0.346 0.287 0.250 0.305

3

40

10

280.4−284.6

9.9−19.9

1.088

9 3 5

40 23 41

10.0−30.0 10 10

279.6−289.7 285.76−291.14 284.7−287.1

9.7−19.8 10.54−20.36 9.39−12.16

0.178 0.103 0.058

4

41

10

285.6−287.1

9.73−11.5

0.295

23 23 23 39, 42

10 10 10 0.1−10

286.2−291.48 285.87−291.59 285.98−291.25 276.62−288.01

10.52−20.45 10.57−20.42 10.68−20.67 4.18−15.31

0.156 0.193 0.245 0.275

41

10.0−20.0

283.4−286.7

9.34−11.5

0.494

3 3 3 41 8 165

0.307

The absolute average relative deviation in temperature (AARD-T) is used to quantify the accuracy of the predicted dissociation temperature

the vapor phase. Therefore, the fugacity of water in the vapor phase can be determined from eq 15. The water fugacity in the liquid phase is calculated based on the correction to the Lewis− Randall rule38 L f w̅

(T , P , x̲ ) = x wγw(T , P ,

x̲ )f wL (T ,

P)

AARD‐T(%) =

(22)

L

where f w is the pure water fugacity gained from PRSV EOS under temperature T and pressure P and γw is the activity coefficient of water from eq 10. In the hydrate phase, the water fugacity is directly gained from eq 17 with the saturated vapor pressure of empty hydrate given as ln Pwsat = A + B ln T + CT + DT −1 + ET −2

(23)

= (11.835 + 2.217 × 10−5T + 2.242 × 10−6T 2)3 − 8.006 × 10−3P + 5.448P 2 (24)

β ,II VW (T , P )

= (17.13 + 2.249 × 10−4T + 2.013 × 10−6T 2)3 10−30NA β ,II NW

i

Ticalc − Tiexp t Tiexp t

(26)

4. RESULTS AND DISCUSSION 4.1. Prediction of the Change in Dissociation Temperature of Methane Hydrates upon Addition of Ionic Liquids. As a validation of the proposed model, we compare the predicted dissociation condition of methane hydrates with addition of IL to the experimental measurements. The experimental data include different combinations of cations (1,3-dimethylimidazolium, 1-ethyl-3-methylimidazolium, 1propyl-3-methylimidazolium, 1-butyl-3-methylimidazolium, and 1-(2-hydroxyethyl)-3-methylimidazolium) and anions (iodide, bromide, chloride, ethylsulfate, bisulfate, methylsulfate, and tetrafluoroborate), constituting a total of 17 systems and 165 points23,39−42 with the inhibitor concentration ranging from 0.1 to 40 wt %, temperature from 273.6 to 291.59 K, and pressure from 1.01 to 20.77 MPa. The overall absolute average relative deviation in temperature (AARD-T %) is 0.31%, as given in Table 2. Note that our model seems to exhibit relatively large error (1.09%) for the system containing the mixture of EMIM-Cl and NaCl. In our previous work43 we found that the prediction accuracy when only NaCl is present is 0.24%, compared to 0.35% (Table 2) when only EMIM-Cl is present. Since only three data points are available in the literature for the mixture of EMIM-Cl and NaCl, it is possible that the experimental data is less reliable for this system. For the systems examined, the IL usually has a small effect in reducing the dissociation temperature of methane hydrate.

β ,I VW (T , P )

β ,I NW

∑

where Ndata is the number of data points.

The values of coefficients A to E for structure I are 28.968, 0.12879, 2.1434, −6003.9, and 100002, respectively.35 The saturated fugacity coefficient is assumed to be unity. The molar volume of empty hydrate in structures I and II suggested by Klauda and Sandler34 is used

10−30NA

100% Ndata

− 8.006 × 10−3P + 5.448P 2 (25)

β,II where NA is the Avogadro constant and Nβ,I W = 46, NW = 36 are the number of water molecules per unit lattice.

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Figure 1 shows the data for the addition of 10 wt % of 1-butyl3-methylimidazolium methylsulfate. The reduction in dissoci-

Figure 3. Experimental three phase equilibrium conditions of 10 wt % MMIM-I39 (blue asterisk), EMIM-I39 (red triangle), PMIM-I23 (orange diamond), and BMIM-I23 (violet square) in methane hydrate system and pure methane hydrate52−62 system (black circle). Corresponding prediction results are shown in solid lines of the same color. The inhibition power increases with the decrease of alky chain length, i.e., MMIM-I > EMIM-I > PMIM-I > BMIM-I.

Figure 1. Experimental three phase equilibrium conditions of 10 wt % BMIM-MeSO441 (red square) in the methane hydrate system and pure methane hydrate52−62 system (black circle). Corresponding prediction results are shown in solid lines of the same color.

more effective ILs and identify the key factors that determine the inhibition capability of ILs. 4.2. Screening for the Most Effective IL Inhibitors. Here, predictions are made for the phase behavior of methane hydrate with ionic liquids for which no experimental data are yet available. The analysis of the results may help identify the key factors for determining the inhibition ability. In this work, 56 cations and 41 anions resulting in 1722 ionic liquids and 574 electrolytes (a complete list of all the species is provided in Tables S1 and S2 of the Supporting Information) are chosen in our investigation. All these ILs and electrolytes are assumed to be thermodynamic inhibitors in our calculations. Note that, while most ILs are inhibitors, some have been shown to be thermodynamic promoters, such as tetra-n-butylammonium (TBA) chloride, 44−47 TBA bromide,46−49 TBA fluoride,46 TBA nitrate,45 and tetra-nbutylphosphonium (TBP) bromide.45,47 The cations TBA and TBP could result in the formation of semiclathrate hydrates50 and, thus, are not considered in this work. The three-phase equilibrium temperatures are determined at 20 MPa with the concentration of IL set to be 0.015 mol % (corresponding to 10 wt % for EMIM-Cl) in all cases. A relatively high pressure of 20 MPa is used because, according to our experience, the degree of inhibition is pronounced at high pressures. Figure 4 illustrates the population distribution (expressed in terms of probability density; i.e., the area underneath each curve is normalized to unity) of the 1722 ionic liquids and 574 electrolytes in terms of their inhibition power (reduction in the dissociation temperature ΔT of methane hydrate). In Figure 4a the population distributions of inhibitors containing the same valence of anions (−1, −2, and −3, respectively) are plotted in separate curves. The similar population distributions (e.g., peak population around ΔT = 4 K) indicates that the inhibition power is not dominated by the type and valence of anions. When plotted in terms of the same valence of cations (Figure 4b), however, there is a clear shift of the population to larger values of the reduction temperature as the valence of the cations increases. For example, ILs containing +2 cations (long dashed orange line in Figure 4b) are usually more effective compared to ILs containing +1 cations (solid purple line). Similarly, electrolytes with +3 cations (see the dot dashed blue

ation temperature of about 1.5 K is correctly predicted by the proposed model. To enhance the inhibition effect, other coinhibitors can be introduced. Figure 2 shows the melting

Figure 2. Three phase equilibrium line of EMIM-Cl + ethylene glycerol (EG) in the methane hydrate system and pure methane hydrate52−62 system. The experimental data40 at different concentrations are shown in black circles (no inhibitor), red squares (5 wt % EG, 5 wt % EMIM-Cl), green diamonds (10 wt % EG, 10 wt % EMIM-Cl), and blue triangles (15 wt % EG, 15 wt % EMIM-Cl). Corresponding prediction results are shown in solid lines of the same color. The dashed lines are the predictions for the corresponding systems without addition of EG.

condition of methane hydrates with the addition of equal weight fractions of 1-ethyl-3-methylimidazolium chloride and ethyl glycerol (EG). With the help of EG, the equilibrium temperature decreases by 4 K in 10 wt % EMIM-Cl plus 10 wt % EG, while it decreases by less than 2 K without EG. The effect of alkyl chain on a cation on the melting condition is illustrated in Figure 3. The experimental data show that IL with a shorter alkyl chain on a cation exhibits a stronger inhibition effect, which is correctly predicted by the proposed model. The results here show that the PRSV + MHV1 + COSMOSAC + vdW-P model is capable of predicting the effect of ILs on the melting conditions of methane hydrates. We therefore take a step forward to use this method to search for 16989



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Figure 4. Probability density distribution, P(ΔT), of ILs resulting in a reduction of the dissociation temperature of ΔT for methane hydrate at 20 MPa and IL concentration of 0.015 mol %. (a) The distribution of ILs and electrolytes containing −1 anions (green dashed), −2 anions (red dotted), and −3 anions (blue dot dashed). (b) The distribution of ILs containing +1 cations (purple solid) and +2 cations (orange long dashed) and electrolytes containing +1 cations (green dashed), +2 cations (red dotted), and +3 cations (blue dot dashed).

Figure 5. Reduction in the dissociation temperature of methane hydrate upon addition of 0.015 mol % of monovalent ionic liquid at P = 20 MPa. The reduction temperatures (green for ΔT > 2.5 K, blue for 2.5 K > ΔT > 0.5 K, and purple for ΔT < 0.5 K) are analyzed in terms of the volume (a), surface area (b), and hydrogen bonding surface area (c) of the cation and anions.

left corners). In contrast, there is no clear dependence on the hydrogen bonding surface area, which is the portion of the molecular surface that could form hydrogen bonds. In this data set, most cations are capable of hydrogen-bonding with water, but the percentage of hydrogen-bonding surface area in the total surface area is small (average 1.7%). On the other hand, the anions have an average area fraction of 67% that form hydrogen bonds with water. Even so, there is no obvious correlation between the inhibition power and the hydrogenbonding surface area of anions (Figure 5c). Therefore, hydrogen bonding may not a primary factor affecting inhibition capability. From the above analysis, the strength of hydration (which is higher for high valent ions and/or small ionic volumes) could be the main factor determining the inhibition power of ILs on the formation of methane hydrates. Strong hydration of ions in the solution may destruct the hydrogen bonding network of water, resulting in a stronger inhibition effect. A simple way to estimate the strength of hydrate is the Born model,51 in which the hydration free energy of a spherical ion is ΔGhyd = [(1/ε) − 1](q2/R), with ε being the dielectric constant of the solvent, q the charge of the ion, and R the radius of ion. Therefore, the strength of hydrate increases with the increasing of ion valence (q) and decreasing of ion volume (4πR3/3).

line in the inset of Figure 4b) are more effective than those with +2 cations (red dotted) and +1 cations (green dashed). Furthermore, the inhibition capability of electrolytes is usually better than that of ILs. For example, the top five best inhibitors are chromium hexafluorophosphate (35.32 K), chromium tetrafluoroborate (31.08 K), chromium perchlorate (26.10 K), chromium trifluoromethanesulfonate (19.34 K), and chromium nitrate (19.14 K). For ILs, the top five best inhibitors are 1,1dimethyl-4,4′-bipyridinium phosphate (10.35 K), 1,1-(1,2ethanediyl)bispyridinium phosphate (9.52 K), 1,3-dimethylimidazolium phosphate (9.01 K), 1,1-(1,2-ethanediyl)bis[3-ethylimidazolium] phosphate (7.60 K), and 1-ethylpyridinium phosphate (7.35 K). The best monovalent ionic liquid as thermodynamic inhibitor is pyridinium chloride (2.59 K). It is worth noting that the inhibition power of the ILs studied in the previous section is in the range of 2.00−3.00 K here. Therefore, the proposed method can be used for screening for more effective IL inhibitors before any actual experiments. Figure 5 shows the predicted reduction in the dissociation temperature from different combinations of monovalent cations and anions. The cations (y-axis) and anions (x-axis) are represented by their volume (Figure 5a), surface area (Figure 5b), and hydrogen-bonding surface area (Figure 5c), respectively. It can be seen that the IL having a small volume and surface area tends to have stronger inhibition effects (lower 16990



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5. CONCLUSIONS The change in dissociation temperature of methane hydrates with addition of ionic liquids is successfully predicted using the PRSV + MHV1 + COSMOSAC + vdW-P model. For inhibitors that do not participate in the solid framework of hydrates, this method does not require input of any experimental data of the inhibitor nor the need for fitting of any additional binary parameters. Therefore, the method can be used to screen for ionic liquid inhibitors for methane hydrate applications before experimental measurements. The key factors affecting the inhibition capability are identified based on this method. The primary factors are the valence number and the molecular size of ionic liquids. Divalent cations/anions often results in a more significant reduction in the dissociation temperature than monovalent cations/anions. Our results provide a useful guidance for developing better thermodynamic IL inhibitors for gas hydrates.

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ASSOCIATED CONTENT

S Supporting Information *

A complete list of cations and anioins and their properties studied in this work is provided. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*Tel.: +886 (0)2 33661369. Fax: +886 (0)2 23623040. E-mail: [email protected] (Shiang-Tai Lin). *Tel.: +886 (0)2 23623296. Fax: +886 (0)2 23623040. E-mail: [email protected] (Li-Jen Chen). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

The authors are grateful for the financial support of this research from the Ministry of Economic Affairs (1025226904000-05-03) and the National Science Council (NSC 102-3113-P-002-01) of Taiwan.

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Prediction of Phase Equilibrium of Methane Hydrates in the Presence

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