Thermodynamic Stability Conditions of Clathrate Hydrates in Methane

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

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Thermodynamic Stability Conditions of Clathrate Hydrates in Methane/Carbon Dioxide + Tetrahydrofuran + Cyclopentane + Water Systems: Experimental Measurement and Modeling Maryam Seif,† Arash Kamran-Pirzaman,*,† and Amir H. Mohammadi‡,§ †

Department of Chemical Engineering, University of Science and Technology of Mazandaran, Behshahr, Iran Institut de Recherche en Genie Chimique et Petrolier (IRGCP), Paris Cedex, France § Discipline of Chemical Engineering, School of Engineering, University of KwaZulu-Natal, Howard College Campus, King George V Avenue, Durban 4041, South Africa

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‡

ABSTRACT: In this communication, experimental hydrate dissociation data for methane + tetrahydrofuran (THF) (0.03 and 0.0555 mole fractions in aqueous solution) + cyclopentane (CP) + water systems are reported in the temperature range from 294.8 to 301.3 K and pressure range from 1.91 to 4.95 MPa, which are measured using an isochoric pressure-search method. Other experimental data were collected from the literature. Then a thermodynamic model for four-phase equilibria, hydrate (H)−aqueous liquid (Lw)−organic liquid (La)−vapor/gas (V), systems composed of water, methane (CH4), carbon dioxide (CO2), and/or CP was developed. The thermodynamic model is based on the solid solution theory of van der Waals−Platteeuw (vdW-P) for the hydrate phase and Peng−Robinson equation of state (P-R EOS) for vapor/gas phase. For calculating the activity coefficient of water and THF in the aqueous phase, the universal quasichemical (UNIQUAC) functional-group activity coefficient (UNIFAC) model is also used. The Langmuir constants of THF and CP are calculated by using the Parrish and Prausnitz equations under this assumption that THF and CP occupy large cavity and CH4 occupies small cavity of structure II hydrate. The calculated Langmuir constants are extended to other systems. Using the vdW-P model, PR EOS, and calculated Langmuir constants, the binary interaction parameters for van Laar, nonrandom two-liquid, and UNIFAC models are calculated. Results show that THF and CP decrease the equilibrium pressure, and by adding both THF and CP into the pure water; these mixtures show better promotion effects in comparison to the individual ones.

1. INTRODUCTION Natural gas alternative resources such as coal-bed methane, tight gas reservoirs, and natural gas hydrates, store a vast volume of gases. Gas hydrate is a massive resource which, if just 15% of it is used, will provide energy for nearly 200 years.1 As water molecules have hydrogen bonds, empty cages form, and these cages are unstable. At conditions of low temperatures and/or high pressures, small molecules (as a guest) such as methane, ethane, or carbon dioxide could physically adsorb into the empty cages made of water (as host). So far, three common structures (I, II, and H) are known as a function of the physical characteristics of guest molecules.2 In the past, these nonstoichiometric ice-like compositions were known as destructive compounds in the oil and gas industries. Researchers have found that these compounds can cause blockage in the oil and gas pipelines.2 Alternately, many useful applications of gas hydrates were reported including gas storage, water desalination, cool-energy storage, carbon dioxide capture, and future potential energy sources in ocean sediments and permafrost sites; therefore, researchers are trying to find effective ways to improve gas hydrate formation conditions. Studies indicate that 1 m3 of gas hydrate can store 170 m3 of natural gas.3−10 © XXXX American Chemical Society

Carbon dioxide is a greenhouse gas and plays a considerable role in climate change. Thus, it is important to separate this gas from flue and industrial gases.11,12 Researchers try to capture and eliminate this gas by gas hydrate formation as a new method. Hydrate formation-based technologies are environmental friendly and have high-energy efficiency.13 On the other hand, the gas hydrate process needs high pressure and low temperature conditions, which are not desirable. Thus, it is important to use gas hydrate promoters.14 Gas hydrate prompters are typically divided into two different types of thermodynamic and kinetic promoters. Thermodynamic promoters change equilibrium conditions, decrease hydrate phase equilibrium pressure, and increase hydrate phase equilibrium temperature. Kinetic promoters raise the gas hydrate formation rate and amount. Thermodynamic promoters are divided into two different kinds based upon their solubility in water (water−soluble and water−insoluble thermodynamic promoters). Tetrahydrofuran, 1-3 dioxane, 1-4 dioxane, Received: September 7, 2018 Accepted: January 15, 2019

A

DOI: 10.1021/acs.jced.8b00804 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

and acetone belong to the first group which do not participate in hydrate crystalline structure and enter into the large cavities of structure II. Tetra-n-butyl ammonium halides (TBAX) are another kind of water-soluble thermodynamic promoters that participate in hydrate crystalline structure. THF and TBAB are two common thermodynamic hydrate promoters. The second category is water insoluble thermodynamic promoters which form structures II or H. Cyclopentane and cyclohexane are two instances of these additives.15 In 1996, Saito et al. studied natural gas hydrate formation with THF, 1,4- dioxane, and acetone promoters. They observed that equilibrium pressure declined in the presence of these promoters.16 Delahaye et al. measured equilibrium conditions of carbon dioxide hydrate in the presence of different concentrations of THF and concluded that with increasing THF concentrations the hydrate pressures decreased.17 Other scientists, Martinez et al. investigated some properties of carbon dioxide + THF + water-like equilibrium conditions, enthalpy, and hydrate number. The THF concentration was between 1 and 16.0 wt % and pressure varied from 0.2 and 2 MPa. They modeled the equilibrium condition by the van der Waals and Platteeuw method with the Redlich−Kwong−Soave equation of state and UNIFAC activity coefficient model for calculating fugacities of hydrate, gas and liquid, respectively. In their paper, they stated THF filled the large cavity of the SII hydrate, and by this assumption, the equilibrium data were predicted. The experimental data and predicted results were in a good agreement. Finally, they concluded that THF + carbon dioxide slurries could be a good mixture for refrigeration application.18 Seo et al. studied methane/ nitrogen + water + cyclical ether (THF, propylene oxide, and 1,4-dioxane) systems. They reported that these cyclical ethers acted as thermodynamic promoters, and THF has a drastic effect than other researched promoters. They also assessed formation conditions of nitrogen hydrate in the presence of THF and observed that by increasing THF concentration in the aqueous solution up to 1 mol %, the promotion effect was increased rapidly, after that it was slow before stoichiometric concentration (5.56 mol %). After 5.56 mol %, the promoting effect slightly decreased.19 In 2001, Fan et al. were the first researchers who investigated cyclopentane hydrate formation without any other gases, and they claimed that CP made a structure II hydrate.20 Recently, Herslund et al. assessed carbon dioxide gas hydrate formation in the simultaneous presence of THF and CP and revealed this system could provide a lower pressure comparing with the individual presence of these additives.21 In 1959, van der Waals and Platteeuw proposed a thermodynamic model for gas hydrates.22 There are several thermodynamic models, which are the extension of vdW-P model, including Parrish and Prausnitz’s model.23 Pirzaman et al. and Illbeigi et al. presented two thermodynamic models for predicting gas hydrate equilibrium conditions in the presence of THF with the use of the activity coefficient model for water and promoter. They reported satisfactory agreement between their model predictions and experimental data.24,25 In comparison with different promoters, THF as watersoluble and CP as water-insoluble components had a suitable result and could decrease hydrate pressure and increase hydrate temperature considerably. There are many articles about the experimental data of individual thermodynamic promoters such as THF and CP with different types of gases, but there is limited information on the simultaneous presence of these promoters. In this work, the question does the mixtures of these hydrate promoters have a better effect or not was the main aim. In this

communication, experimental equilibrium data are reported for four-phases hydrates (H)- aqueous liquid (Lw)-organic liquid (La)-vapor/gas (V) of CH4 in the presence of CP + THF (with concentrations 3 and 5.55 mol %) at T = (294.8 to 301.3) K and P = (1.91 to 4.95) MPa. Then, a thermodynamic model for CH4 and CO2 gas hydrates in individual and simultaneous presence of THF and CP is reported. The thermodynamic model is based on van der Waals−Platteeuw model, Peng−Robinson equation of state, and the universal quasichemical (UNIQUAC) functionalgroup activity coefficients (UNIFAC) model for calculating fugacities in hydrate, gas, and liquid phases, respectively. Finally, experimental and predicted data are compared with each other.

2. THERMODYNAMIC MODEL By equality of fugacity of water in liquid and hydrate phases, hydrate phase equilibrium conditions can be calculated:2 f wL = f wH

(1)

where f represents the fugacity, the subscript w indicates water and superscripts L and H indicate liquid and hydrate phases, respectively. The fugacity of water in the hydrate phase depends on differences of water chemical potentials in hypothetical empty hydrate lattice and filled hydrate lattice:

ij μH − μ MT yz w z zz f wH = f wMT expjjjj w zz j RT (2) k { MT f w is the fugacity of hydrate in empty hypothetical lattice and MT stands for empty hydrate lattice. R, T, and μ are the universal gas constant, temperature, and chemical potential, respectively. Using the van der Waals and Platteeuw model, the chemical potential difference is calculated as follows: μwH − μwMT RT

= −∑ ϑi ln(1 + i

=

∑

∑ Cjmf j ) j

ln(1 +

i

∑ cjmf j )−ϑ

i

j

(3)

In eq 3, vi is the number of cages i per each water molecule within a unit hydrate cell which is different from the structures I and II. vi for small cavity and large cavity of structure I is equal to 1/23 and 3/23 and for structure II is equal to 2/17 and 1/17, respectively.2 Cjm represents the Langmuir constant for component j and lattice type m, and f j is the fugacity of component j, a guest molecule in the hydrate phase. For determining Langmuir constants, Parrish and Prausnitz proposed correlations.26 Water fugacity is calculated by the following expression:27 f wMT = PwMT exp

vwMT(P − PwMT) RT

(4)

MT where PMT w , vw and P are the vapor pressure, the partial molar volume of water in empty hydrate lattice, and the pressure, respectively.27 Water fugacity in the aqueous phase can be calculated as:

ij v l (P − Pwsat) yz zz f wL = X wLγwPwsat expjjjj w zz RT (5) { k L sat xw, γw and Pw are the mole fraction of water in the liquid phase, the activity of water, and saturated pressure of water, respectively. xLw is calculated as follows: x wL = 1 − xg − x THF B

(6) DOI: 10.1021/acs.jced.8b00804 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

Table 1. UNIFAC, van Laar, NRTL, and UNIQUAC Activity Coefficient Modelsa model

binary parameters

equations

ln γi = ln γic + ln γi r ln γic = ln

ϕi xi

(8)

ϕ θ z qi ln i + li − i 2 xi ϕi

+

z li = (ri − qi) − (ri − 1) 2 xiri ϕi = ∑j xjrj (11)

θi = UNIFAC30

j

(9)

(10)

xiqi ∑j xjqj

r

ln γi =

without binary parameters

N

∑ xjlj

∑

(12) vk(i)(ln Γk

− ln Γ(ki))

ÅÄÅ yz ij ÅÅ ln Γk = Q kÅÅÅÅ1 − lnjjjj∑ ΘmΨmkzzzz − ÅÅ z j ÅÅÇ { km Q mX m Θm = ∑n Q nX n (15) k

Xm =

ÑÉÑ ΘmΨkm ÑÑÑ ÑÑ ∑n ΘnΨnm ÑÑÑÑ ÑÖ

(13)

∑ m

(14)

∑i xivm(i) ∑i ∑n vn(i)xi

i a y Ψmn = expjjj− mn zzz k T {

(16) (17)

ij Aijxi yzz zz ln γi = Aijjjjj1 + j Aji xi zz (18) { k i = 2, j = 1 or i = 1, j = 2 ÑÉÑ ÅÄÅ 2 ÑÑ ÅÅ ji G τijGij zyz ÑÑ ij j 2Å Å z j ÑÑ Å ln γi = xj ÅÅτjijj z + z 2 ÑÑ ÅÅ j xi + xjGji z ( x + x G ) j i ij Ñ ÑÑÖ ÅÇÅ k { i = 2, j = 1 or i = 1, j = 2 gij − gjj τij = ; ln Gij = − αijτij (20) RT −2

van Laar31

Aij, Aji

NRTL32

gij, gji

ij θ z ri yz q ln i + ϕjjjjjli − l jzzzz − qi ln (θi + θτ j ji) 2 i ϕi rj { k τij zyz ji τji zz + θjqijjjj − zz j θi + θτ θ + θτ j ji j i ij { k i = 2 j = 1 or i = 1 j = 2 uij − ujj xiqi xiri ln τij = − ; ϕi = ; θi = ; RT xiri + xjrj xiqi + xjqj

ln γi = ln

UNIQUAC32

(19)

Uij,Uji

li =

ϕi xi

+

z (ri − qi) − (ri − 1) 2

(21)

(22)

Z = 10 a

Terms: xi and xj, mole fractions of component i and j; ri, relative van der Waals volume; qi, measure of molecular surface-areas; Z: coordination number; vli and vlj, molar volume of liquid, cm3/mol; c, combinatorial term of UNIFAC activity coefficient model; r, residual term of UNIFAC activity coefficient model; v(i) k , number of groups of type k in molecule i; Qk, UNIFAC surface-area parameter; Rk, UNIFAC group volume parameter; amn, UNIFAC group−group interaction parameter; αij, NRTL parameter.

xg is the mole fraction of gas in water, which is expressed as27 xi =

water activity coefficient which is approximately unity for systems consisting of gas + water + CP, but for a system containing THF, as THF is water-soluble, it should be calculated.29 In this study, different activity coefficient models such as UNIFAC, van Laar, nonrandom two-liquid (NRTL), and UNIQUAC were used, and their expressions are listed in Table 1.30−32 For calculating the fugacity of gas, Peng−Robinson equation of state (PR EOS) is used.33 In cubic equations of state, the

fi V i∞P RT

( )

Hi w exp

(7)

where Hiw is Henrỳs constant of gas in water obtained from the Krichevsky correlation, and V∞ i is the infinite partial molar volume.28 THF is soluble in water, and it is necessary to deduct the amount of THF in liquid water.24 γw is the C



Article

Table 2. Langmuir Constant Parameters for CH4 and CO226 structure I

structure II

small cavity

large cavity

small cavity

large cavity

gas

A ×(10 )

B

A ×(10 )

B

C ×(10 )

D

C ×(10 )

D

CH4 CO2

0.7228 0.2474

3187 3410

23.35 42.46

2653 2813

0.2207 0.0845

3453 3615

100 851

1916 2025

3

3

sat fTHF = x THFγTHFPTHF

A′

CH4 CO2

147.788 69.4237

a

× (1 + C large,THFfTHF + C large,CPfCP )−nlarge ] − 1 = 0

where g represents the gas. 2.1. Model Parameters. For determining Langmuir constants, Parrish and Prausnitz presented the following equations. Constants A, B, C, and D are different for various hydrate formers:26

C large =

1 N

∑

(26)

i

Piexp − Pical Piexp

component

name

main no.

second no.

v(i) k

Rk

Qk

water (1) THF (2)

H2O CH2 CH2O

7 1 13

16 2 25

1 3 1

0.92 0.6744 0.9183

1.4 0.540 0.780

THF CP

14.3873 43.1870

4.0963 3.3877

compoound

critical temperature (K)

critical pressure (MPa)

acentric factor

CH4 CO2 CP

190.4 304.21 511.8

4.6 7.383 4.502

0.011 0.2236 0.194

6003.9 yz i zz PwMT = 0.1 × expjjj17.44 − T { k

Table 3. Langmuir Coefficient Parameters for THF and CP D ×(103)/K

26 27

Structure I:

Table 3 reports the aforementioned constants.

C/K bar−1

0.018616 0.000478857

7258.2 i Pwsat = 10−5 expjjj73.649 − − 7.3037 ln T T k y + 4.1653 × 10−6 × T 2zzz (29) { MT MT In eq 4, there are two parameters, Pw and vw that are different in hydrate structures, which are defined as follows:27

(27)

component

−52.2952 −21.6694

Constants are given in Table 4.26,27 The UNIQUAC activity coefficient model parameters are presented in Table 5.30 Psat W is water saturated pressure, which is calculated using the following equation:27

In Table 2, Langmuir constants of CH4 and CO2 are reported.26 Since THF and CP are two hydrate formers and fill the large cavity of SII hydrate, it is important to calculate their Langmuir constants. As the experimental data of CH4 + CP/THF (0.0556 mole fraction) + water system were known, by using van der Waals and Platteeuw model and eq 26 and by the following equation which is called objective function, the data were substituted and then eq 27 was minimized. Finally, two unknown parameters C and D were estimated: OF =

ref

Table 6. Critical Temperatures, Critical Pressures and Acentric Factors of CH4, CO2, and CP34

(25)

C iDy expjjj zzz T kT {

D′/K−1

Calculated as

(24)

Csmall

−5768.3 −3.7964 × 1000

C′/K−1

Table 5. UNIFAC Group Volume and Surface- Area Parameters for Water (H2O) + THF ((CH2) 3CH2O)29

)

A iBy = expjjj zzz T kT {

B′/K

Hi w = 10(A′+ B′/ T + C′ log(T ) + D′T )

)

(

gas component

(23)

xTHF, γTHF, Psat THF, and vTHF are mole fraction, activity coefficient, saturated pressure, and molar volume of THF. The final equation for calculating equilibrium pressure of gas hydrate at a given temperature is simplified as below: ÄÅ ÉÑ sat ÅÅÅ P MTexp ϑsat ÑÑÑ w (P − Pw ) ÅÅ w ÑÑ RT ÅÅ ÑÑ ÅÅ ÑÑ × [(1 + Csmall, gfg )−nsmall L sat ÅÅÅ x Lγ P sat exp ϑw(P − Pw ) ÑÑÑ ÅÅ w w w ÑÑ RT ÅÇ ÑÖ

(

3

Table 4. Constants A′-D′ in Henrỳs Equationa

critical parameters and acentric factors should be used.34 Another equation is for calculating the fugacity of THF:29 sat ij v (P − PTHF ) yzz expjjj THF zzz j RT k {

3

(30)

−5 −6 2 ϑMT w = (11.835 + 2.217 × 10 T + 2.242 × 10 T )

×

10−20NA NwMT

− 8.006 × 10−9P + 5.448 × 10−12P (31)

6017.6 yz i zz PwMT = 0.1 × expjjj17.332 = T { k

In eq 7, Hiw is Henry’s constant of gas in water, which is calculated as28 Hi w = 10(A′+ B′/ T + C′ log(T ) + D′T )

Structure II:

(28) D

(32)



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Table 7. Purities and Suppliers of CH4, THF, CP and Water chemical

purity (mole fraction)

supplier

methane tetrahydrofuran cyclopentane water

0.9995 >0.98 >0.98 distilled water

Air Product Merck Merck laboratory made

Table 11. Average Absolute Deviation Percent of Hydrate Dissociation Pressure (AADP) for CH4 + CP + Water System

0.03 mole fraction

0.0555 mole fraction

T/K

P/MPa

294.9 299.5 301.3 294.8 299.3 301.3

1.91 4.01 4.95 1.99 3.96 4.84

Table 9. Van Laar, NRTL, and UNIQUAC Binary Interaction Parameters for Water (1) + THF (2) System, J/mol activity coefficient model

A12

A21

αij

van Laar NRTL UNIQUAC

0.36 2.2490 2.55T + 793.2644

3.022 30.91 −0.7096T − 50.9502

0.3012

−4 −6 2 ϑMT w = (17.13 + 2.249 × 10 T + 2.013 × 10 T

+ 1.099 × 10−9T 2)

10−20NA NwMT

− 8.006 × 10−9P

+ 5.448 × 10−12P

(33)

where NA is Avogadro’s number and NMT w is the number of water molecules per hydrate cell, respectively. In eqs 29 to 33 temperatures and pressures are in K and bar, respectively. Knowing values of critical temperatures, critical pressures and acentric factors are important to the equation of state. In Table 6, the values are reported.34 The amounts of THF molar volume and saturation pressure, which are in cm

3

mole

(34)

sat PTHF = 10(4.12118 − (1202.942/(T − 46.818)))

(35)

AADP%

no. of data points

ref

0.16−7.31

3.42

9

38

4. RESULT AND DISCUSSION 4.1. Experimental Result. Table 8 displays the experimental data on four phases H−Lw−La−V for the water + CH4 + CP + THF system. In this work, only two concentrations of THF, 0.03 and 0.0555 mole fractions in water were studied. 4.2. Modeling Result. Equilibrium conditions of three phases H−Lw−V/G and four phases H−Lw−La−V/G for CO2/CH4 hydrate in the presence and absence of THF and CP were modeled by using the vdW-P model. THF is a soluble

and bar, respectively are given as29

vTHF = 0.0899T + 55.104

pressure range/MPa

3. EXPERIMENTAL SECTION 3.1. Materials. In Table 7, the information for purities and suppliers of the materials that were used in this study is reported. Aqueous solutions were prepared by using an accurate analytical balance (AND) with an uncertainty of ±0.0001 g. 3.2. Apparatus. The experiments of hydrate formation were performed in a 300 cm3 stainless steel reactor. The reactor has a magnetic stirrer which agitates the fluids and hydrate crystals. The coolant consists of water and ethylene glycol as antifreeze that is circulated by a circulation pump and transfers water and ethylene glycol through jacket and reactor. The circulator temperature is adjusted by a device. A Pt-100 thermometer is used for measuring the temperature with the accuracy better than 0.1 K, and a pressure transmitter is utilized to measure the cell pressure with an accuracy of 0.05 MPa. A computer software receives the data on a PC computer. 3.3. Experimental Method. An isochoric pressure-search method was used to perform the measurements. First, the hydrate cell was evacuated by vacuum pump. Next, a prepared aqueous solution and organic liquid (100 cm3) were introduced into the cell. The cell was then pressurized to a desired pressure by methane gas. After that it was cooled down, and the magnetic agitator was turned on. When the gas hydrate completely formed, the cell temperature was slowly increased step by step until hydrate crystals dissociated. The pressure−temperature diagram was then plotted. The point at which the cooling and heating curves intersect was considered as the hydrate dissociation point. The dissociation temperatures and pressures uncertainties were estimated to be ±0.1 K and ±0.05 MPa, respectively. The reliability of the experimental method was investigated earlier.

Table 8. Experimental Hydrate Dissociation Data for CH4 + CP + THF + Water System THF aqueous solution

temp/K 282.15−301.9

Table 10. Average Absolute Deviation Percent of Hydrate Dissociation Pressure (AADP) for CH4+ THF+ Water System AADP%a temp range/K

pressure range/MPa

mole fraction of THF in aqueous solution

UNIFAC

van Laar

NRTL

UNIQUAC

no. of data points

ref

289.54−303.01 292.16−302.46 293.11−306.22 277.9−305 292.77−306.23

2.05−14 2.02−8.91 2.05−14.04 0.33−12.5 2.05−14.04

0.0107 0.03 0.05 0.0556 0.1008

5.43 4.39 7.60 12.67 12.57

21.82 4.16 6.92 12.91 4.62

4.14 3.70 7.51 12.89 11.38

2.65 2.44 6.10 13.34 7.30

10 4 9 14 9

36 19 36 37 36

a

AADP is calculated as follows: n

∑i = 1 AADP =

Piexp − Pical Piexp

n

cal where Pexp i ,Pi and n are the experimental and calculated/predicted pressures for component i and number of data points, respectively.

E



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Table 12. Average Absolute Deviation Percent of Hydrate Dissociation Pressure (AADP) for CO2 + THF + Water System AADP% temp range/K

pressure range/MPa


UNIFAC

van Laar

NRTL

UNIQUAC

no. of data points

ref

272.65−287.05 275.05−289.65 279.75−290.95 280.35−291.05 297.7−291.1

0.21−4.08 0.2−4.12 0.35−3.86 0.27−3.82 0.18−3.17

0.01 0.02 0.03 0.05 0.0556

39.6 40.56 22.94 17.20 4.95

58.30 43.14 19.31 12.72 14.30

27.07 25.35 12.60 12.50 14.68

52.80 48.61 33.51 26.27 16.18

6 6 8 7 15

32 32 32 32 33

THF (0.0556 mole fraction) were calculated and these are listed in Table 9. Using the aforesaid constants and parameters, equilibrium pressures were estimated, which are presented in Tables 10−15 and Figures 1−6 and are compared with experimental data.2,19,32,36−39 Table 10 and Figure 1 show the model results for CH4 + THF hydrates. As can be observed in Figure 1, THF acts as thermodynamic promoter and at particular temperature, equilibrium pressure of CH4 hydrate decreases in comparison with CH4 hydrate in the absence of the promoter. At low temperatures, equilibrium pressure decreases approximately 0.4 MPa, and at high temperatures, it decreases to near 1 MPa. Furthermore, it could be concluded that by using THF, there is a slight decrease in concentrations between 0.01 and 0.0556 mole fractions. Regarding the AADP% calculated in Table 10, the assumption that THF changes the CH4 hydrate structure and fills the large cavity of structure II is found to be correct, and the thermodynamic model using all activity coefficient models yields good

Table 13. Average Absolute Deviation Percent of Hydrate Dissociation Pressure (AADP) for CO2 + CP + Water System temp/K

pressure /MPa

AADP%

no. of data points

ref

284.6−291.6

0.49−2.58

5.38

5

38

component in water, thus it is important to calculate the activity coefficient of water and THF.29 For this reason, the UNIFAC activity coefficient model was used. It is also important to estimate Langmuir constants.15,24,35 In this study, by using eq 27 and experimental literature data for the systems of water + CH4 + THF (0.0556 mole fraction) and water + CH4 + CP, Langmuir constant parameters were optimized. The method was explained in section 2.1. There are several activity coefficient models for the systems of THF + water, such as van Laar, NRTL, UNIQUAC, etc. In this study, using the vdW-P model and PR EOS and Langmuir constants, the binary interaction parameters of van Laar, NRTL, and UNIQUAC activity coefficient models for water + CH4 +

Table 14. Average Absolute Deviation Percent of Hydrate Dissociation Pressure (AADP) for CH4 + THF + CP + Water System AADP% temp/K

pressure/MPa


UNIFAC

van Laar

NRTL

UNIQUAC

no. of data points

294.9−301.3 294.8−301.3

1.91−4.95 1.99−4.84

0.03 0.0555

6.70 4.76

17.70 18.16

7.30 5.15

13.35 7.01

3 3

Table 15. Average Absolute Deviation Percent of Hydrate Dissociation Pressure (AADP) for CO2 + THF + CP + Water System AADP% temp/K

pressure/MPa


UNIFAC

van Laar

NRTL

UNIQUAC

no. of data points

ref

285.2−293.2

0.42−2.92

0.0555

11.84

23.72

7.85

21.81

5

39

Figure 1. Experimental2,19,36,37 and calculated/predicted hydrate dissociation conditions for water + CH4 + THF system. Symbols represent experimental data: ⧫, pure water;2 ▲, 0.0107 mole fraction THF;36 ∗, 0.03 mole fraction THF;19 +, 0.05 mole fraction THF;36 ●, 0.0556 mole fraction THF;37 ■, 0.1008 mole fraction THF.36 Curves represent modeling results. F



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Figure 2. Experimental2,38 and calculated/predicted hydrate dissociation conditions for water + CH4 + CP system. Symbols represent experimental data: ◆, pure water2; ▲, CP38. Curves represent modeling results.

Figure 3. Experimental2,32 and calculated/predicted hydrate dissociation conditions for water + CO2 + THF system. Symbols represent experimental data: ◆, pure water2 ; ▲, 0.01 mole fraction THF32; ∗, 0.02 mole fraction THF32; ●, 0.03 mole fraction THF32; +, 0.05 mole fraction THF32; ■, 0.0556 mole fraction THF32. Curves represent modeling results.

on CH4 and CO2 hydrates depend on the THF concentrations up to a 0.01 mole fraction. This effect is considerable and after the stoichiometric concentration (0.0556 mole fraction), the promotion effect slightly decreases. The hydrates of CH4/CO2 + the mixture of thermodynamic promoters of THF + CP were finally modeled. For CH4 + CP + THF aqueous solution, the experimental data are reported in Table 8, and for the CO2 + CP + THF aqueous solution (0.0555 mole fraction), the experimental data are reported in ref 39. The Langmuir constants which were calculated previously are used and it is assumed that the mixture of promoters enters the large cavity of structure II, and CH4 or CO2 fills the small cavity. As it can be observed in Table 14, the model results for both concentrations of 0.03 and 0.0555 mole fractions are in acceptable agreement with experimental data unless the van Laar activity coefficient model is used. In Table 15, for the CO2 + CP + THF (0.0555 mole fraction) + water system, the experimental data and the model results are in satisfactory agreement, but the AADP% is high when the van Laar activity coefficient model is used.

results. Table 11 and Figure 2 show the results for the CH4 + CP + water system. As can be seen in Table 11, experimental and prediction results are in good agreement. CP fills the large cavity and methane fills the small cavity of the structure II hydrate. Figure 2 shows that CP acts as CH4 hydrate promoter and at low temperatures, the equilibrium pressure decreases 0.6 MPa but at high temperatures, it decreases more. The results for CO2 + THF hydrate are indicated in Table 12 and Figure 3. This additive could act as a thermodynamic promoter for CO2 hydrate and at particular temperatures, the equilibrium pressure decreases almost 0.3 MPa, and by increasing THF concentration (0.01−0.0556 mole fraction), the promotion effect increases. As can be noticed in Table 12, the lowest AADP is observed for CO2 + THF (0.0556 mole fraction in aqueous solution) hydrate. THF and CO2 molecules are assumed to occupy the large and small cavities of the structure II hydrate, respectively.19,35,37 In Table 13 and Figure 4, it can be observed that for CO2 + CP hydrate, CP acts as the thermodynamic promoter. The assumption is that, CP enters the large cavities of the structure II hydrate. In Figures 1 and 3, clearly the promotion effects of THF G



Article

Figure 4. Experimental2,39 and calculated/predicted hydrate dissociation conditions for water + CO2 + CP system. Symbols represent experimental data: ◆, pure water2; ▲, CP39. Curves represent modeling results.

Figure 5. Experimental2,19,36-3738 and calculated/predicted hydrate dissociation conditions for water + CH4 + THF + CP system. Symbols represent experimental data: ◆, pure water2; ▲, 0.0107 mole fraction THF36; ∗, 0.03 mole fraction THF19; +, 0.05 mole fraction THF36; ●, 0.0556 mole fraction THF37; ■, 0.1008 mole fraction THF36; ×, CP38; □, CP+ 0.03 mole fraction THF; ○, CP+ 0.0555 mole fraction THF. Curves represent modeling results. H



Article

Figure 6. Experimental2,32,39 and calculated/predicted hydrate dissociation conditions for water + CO2 + THF + CP system. Symbols represent experimental data: ◆, pure water2; ▲, 0.01 mole fraction THF32; ∗, 0.02 mole fraction THF32; +, 0.03 mole fraction THF32; ●, 0.05 mole fraction THF32; ■, 0.0556 mole fraction THF32; ×, CP39; ○, CP + 0.0555 mole fraction THF39. Curves represent modeling results.

However, the model shows relatively large deviations when the van Laar activity coefficient model is used.

Figure 5 shows that THF and CP are thermodynamic promoters, and the hydrate equilibrium pressures decrease. CP is a more effective promoter as compared with THF. There is a substantial decrease in hydrate equilibrium pressure due to presence of the mixture of THF + CP as compared with single promoters. In Figure 6, it can be observed that THF and CP are effective thermodynamic promoters for the water + CO2 system, and the promotion effect of CP is higher than that of THF.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Arash Kamran-Pirzaman: 0000-0002-4073-4880 Amir H. Mohammadi: 0000-0002-2947-1135

5. CONCLUSION In this work, experimental and modeling investigations were done on CH4/CO2 hydrate equilibrium conditions in the simultaneous presence of THF and CP thermodynamic promoters. The experimental hydrate dissociation data for CH4 + CP + (0.03 and 0.0555 mole fraction) THF + water system are reported which were measured using an isochoric pressure search method. THF and CP show important thermodynamic promotion effects. This effect is more considerable when both THF and CP are used simultaneously. Satisfactory agreement is observed between model results and experimental data.

Notes

The authors declare no competing financial interest.

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REFERENCES

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