Application of Extended UNIQUAC Activity Coefficient Model for

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

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Application of Extended UNIQUAC Activity Coefficient Model for Predicting the Clathrate Hydrate Stability Conditions Fatemeh Sharifi,†,⧫ Jafar Javanmardi,*,† Sara Aftab,‡ Arezoo Azimi,† and Amir H. Mohammadi*,§ †

Department of Chemical, Petroleum and Gas Engineering, Shiraz University of Technology, Shiraz, Iran Department of Chemical Engineering, School of Chemical and Petroleum Engineering, Shiraz University, Shiraz, Iran § Discipline of Chemical Engineering, School of Engineering, University of KwaZulu-Natal, Howard College Campus, King George V Avenue, Durban 4041, South Africa Downloaded via UNIV PARIS-SUD on May 7, 2019 at 13:48:40 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

‡

ABSTRACT: The inhibition of gas hydrate (clathrate hydrate) formation plays an important role in petroleum industries. A way to prevent this problem is injecting chemical inhibitors to the transportation pipelines. Two typical kinds of chemical inhibitors are thermodynamic and kinetic inhibitors. The main goal of the current work is to provide a thermodynamic model without using any adjustable parameters for prediction of the dissociation conditions of hydrate for pure and mixed gases including several thermodynamic inhibitors of ethylene glycol (EG), methanol (MeOH), potassium chloride (KCl), calcium chloride (CaCl2), and sodium chloride (NaCl). For this purpose, application of the extended UNIQUAC activity coefficient model along with the van der Waals-Platteuw solid solution theory has been proposed. A comprehensive literature survey has been performed to provide a complete set of experimental data, and 1455 data points have been provided. Comparing the current model results with the experimental data reported in literature, the average absolute deviations (AAD) is 0.50 K which shows the accuracy of the results of the model developed in the current study. alcohol being also included. Englezos and Bishnoi20 modeled the gas hydrate dissociation conditions for systems including electrolyte solutions considering the fact that water chemical potential is equal in both existing phases. Nasrifar et al.21 proposed a combining rule to model hydrate formation for systems containing mixed electrolytes and alcohols. Javanmardi et al.22 developed a straightforward hydrate formation prediction method without using multiphase flash calculations for systems containing electrolyte solutions. Najibi et al.23 reported the experimental dissociation data for systems including methane, water, thermodynamic inhibitor, and salt in the pressure range of 6.89−29 MPa. They applied the Valderrama modification of the Patel−Teja (VPT) equation of state (EoS) combined with the modified Debye−Hückel term to model the studying systems. Jiang et al.24 studied the hydrate dissociation conditions of methane, ethane, and propane in the presence of different alcohols and salts by applying the ion-based SAFT2 coupled with van der Waals and Platteeuw theory. Valavi and Dehghani25 developed a model on the basis of the modified PHSC EoS. Zare et al.26 investigated the effects of five ionic liquids on methane hydrate systems by applying the cubic

1. INTRODUCTION Gas hydrates, or clathrate hydrates, are made of water molecules (host) and gas and/or some volatile liquid molecules (guest). According to the guest molecule(s) size, three typical structures, sI, sII, and sH, can form.1 In spite of the fact that gas hydrates are useful in different fields such as gas storage and transportation,2−4 desalination of the seawater,5 gas separation,6−8 refrigeration and air conditioning systems9,10 and greenhouse gases capturing,11 they can also cause blockage of the natural gas pipelines. Consequently, numerous investigations have been performed in order to inhibit formation of gas hydrates using thermodynamic inhibitors. Thermodynamic inhibitors shift the hydrate formation temperature and pressure to lower and higher values, respectively. Thermodynamic inhibitor molecules or ions change the activity of water; therefore, the hydrocarbon and water thermodynamic equilibrium will be changed. In addition, they can solve a little amount of associated hydrate. Alcohols and some electrolytes are known as thermodynamic inhibitors.12 van der Waals and Platteeuw proposed a solid solution theory representing the chemical potential of water in the hydrate phase13 which was later generalized by Parrish and Prausnitz14 and then extended by Ng and Robinson15 and Holder et al.16 etc. Afterward, different other models were published by Anderson and Prausnitz17 and Moshfeghian and Maddox18 which were based on the calculation of water fugacity and enthalpy of hydrate formation, respectively. Hammerschmidt19 used an empirical model to predict hydrate formation with © XXXX American Chemical Society

Special Issue: Celebrating Our High Impact Authors Received: December 1, 2018 Accepted: April 5, 2019

A

DOI: 10.1021/acs.jced.8b01149 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

square well EoS along with the theory of van der Waals− Platteeuw. Delavar et al.27 reported the effect of methanol on gas hydrate systems including CH4, C2H6, C3H8, C4H10, N2, H2S, and CO2 using the UNIQUAC activity coefficient model applied to the liquid phase while the SRK EoS and HuranVidal (HV) mixing rule were used for the gas phase. Mohammadi et al.28 studied the hydrate dissociation temperature of the systems including H2S along with different inhibitors including alcohols (methanol and ethanol), salts (NaCl, KCl and CaCl2), and ethylene glycol (EG) by applying the extended UNIQUAC activity coefficient model. The interaction parameters of the activity model were fitted using the experimental H2S hydrate dissociation data. Delavar et al.29 studied systems containing CH4, C2H6, C3H8, CO2, and H2S hydrates along with inhibitors applying the original UNIQUAC activity coefficient model. Despite the simplicity of the proposed model, the results were highly accurate. Cha et al.30 reported the effects of piperidinium and morpholinium on carbon dioxide hydrate formation conditions. Kamari et al.31 investigated the CO2 hydrate dissociation conditions in the presence of KBr, CaBr2, MgCl2, HCOONa, and HCOOK aqueous solutions applying the Valderrama modification of the Patel-Teja EoS for the gas phase and the UNIQUAC activity coefficient model along with the Debeye-Huckel method for calculation of the water activity coefficient. In this work, the extended UNIQUAC activity coefficient model along with the van der Waals-Platteeuw theory has been applied to predict the hydrate dissociation (formation) conditions of the studying systems which contain (methanol and ethylene glycol as well as different salts (KCl, NaCl, and CaCl2) as thermodynamic inhibitors. For this purpose, a comprehensive database was collected from the literature. The parameters of the activity coefficient model have been collected from the literature based on the optimization of VLE data. Table 1 shows the properties of the studied components.

Table 2. Properties Needed for Calculation of the Chemical Potential Difference of Water1 parameter

( ) ( molJ·K ) J Δhw0 ( mol ) ΔCpw0

Tc (K)

Pc (kPa)

ω

CH4 C2H6 C3H8 CO2 N2 H2S C4H10

190.56 305.32 369.83 304.19 126.1 373.53 408.14

4599 4872 4248 7382 3394 8963 3648

0.0115 0.0995 0.1523 0.2276 0.0403 0.0827 0.1770

937

1297

38.12

38.12

1025

1389

r

q

H2O Na+ K+ Ca2+ Cl− CH3OH C2H5OH MEG

0.920 1.4034 2.2304 3.870 10.386 3.3496 5.88 5.4996

1.4 1.1990 2.4306 1.48 10.197 3.7386 5.88 7.0797

no. of cavity

∑ m=1

ij υm lnjjjj1 + j k

no. of comp

∑ i=1

yz Cmifi zzzz z {

(3)

where R represents the universal gas constant, 8.314 J/(g·mol·K), T stands for temperature and f i is the fugacity of molecules in the gas phase. υm denotes the number of type m cavities per the number of water molecules existing in a unit cell of the hydrate phase and f is the gas fugacity. Cmi represents the Langmuir constant of the ith gas species in the m type cavity. The no. of comp. and no. of cavity show the number of components and the number of cavities in a unit cell of the hydrate lattice, respectively. To calculate the Langmuir adsorption constants, the cell theory of Lennard-Jones-Devonshire1 can be used as follows: Cmi =

4π kT

∫0

∞

i −ω(r ) yz 2 zzr dr expjjjj z k kT {

(4)

where r is the distance of the guest molecule from the cavity

( kJ )

center, k stands for the Boltzmann constant, 1.38 × 10−23

and T is temperature. ω(r) demonstrates the symmetric cell potential which is calculated using the Kihara potential function as follows:1 ÄÅ 12 ÉÑ ÅÅ σ i 10 a 11yz σ 6 ij 4 a 5yzÑÑÑ Å j Å jjδ + ω(r ) = 2εZÅÅ 11 jjδ + δ zz − δ zzÑÑ ÅÅÇ R′ r k R′ { R′5 r k R′ {ÑÑÑÖ É ÅÄ −N −N Ñ 1 ÅÅÅÅij r a yz r a yz ÑÑÑÑ ij N zz − jj1 + zz Ñ δ = ÅÅjj1 − − − N ÅÅÇk R′ R′ { R′ R′ { ÑÑÑÖ k

(5)

(6)

where N is 4, 5, 10, or 11. The number of water molecules available in a cavity is shown by z (coordinate number). σ is the distance of the core at zero potential (ω = 0), and ε defines the characteristic energy which is the maximum attractive potential at r = 6 2 σ . R′ stands for the free cavity radius and a is the spherical core radius. In this work, f i is calculated using the Peng-Robinson EoS.32 Using the classic thermodynamics, the left-hand side of eq 2 is rearranged as follows:16

(1)

Subtracting the water chemical potential in the empty hydrate phase (μβw) from both sides of eq 1, the following expression is obtained: Δμwβ − I/L = Δμwβ − H

structure II

component

Δμwβ− H = RT

2. THERMODYNAMIC MODEL The proposed thermodynamic model is based on the van der Waals Platteeuw theory13 which applies the equality of water chemical potential (μw) in ice (I) or liquid (L) and in hydrate (H) phase as follows: μwI/L = μwH

structure I

Table 3. Pure Component Parameters for the Extended UNIQUAC Activity Coefficient Model33−36

Table 1. Critical Properties and Acentric Factors of the Studied Compounds1 compound

J mol

Δμw0

(2)

The right side of the eq 1 is described as follows: B



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Table 4. Binary Interaction Parameters, u0ij = u0ji for the Extended UNIQUAC Activity Coefficient Model33−36 H2O Na+ K+ Ca2+ Cl− CH3OH EG

H2O

Na+

K+

Ca2+

Cl−

CH3OH

MEG

0 733.286 535.023 166.7021 1523.39 259.64 249.7378

733.286 0 −46.194 384.0513 1443.23 1723.57 292.9922

535.023 −46.194 0 1469.491 1465.18 667.88 N.A.

166.7021 384.0513 1469.491 2879.923 2316.383 N.A. N.A.

1523.39 1443.23 1465.18 2318.383 2214.81 1637.99 N.A.

259.64 1723.57 667.88 N.A. 1637.99 373.43 N.A.

249.7378 292.9922 N.A.a N.A. N.A. N.A. 339.9663

a

N.A. means this parameter is not available for this pair.

Table 5. Binary Interaction Parameters, utij = utji, for the Extended UNIQUAC Activity Coefficient Model33−36 H2O Na+ K+ Ca2+ Cl− CH3OH EG

H2O

Na+

K+

Ca2+

Cl−

CH3OH

MEG

0 0.4872 0.9936 −5.7699 14.631 −0.07 0.71268

0.4872 0 0.1190 −3.3839 15.635 21.729 0.48719

0.9936 0.1190 0 −3.31 15.329 0.458 N.A.

−5.7699 −3.3839 −3.31 0 9.2428 N.A. N.A.

14.631 15.635 15.329 9.2428 14.436 14.48 N.A.

−0.07 21.729 0.458 N.A. 14.48 −0.728 N.A.

0.71268 0.48719 N.A.a N.A. N.A. N.A. 0.56247

a

N.A. means this parameter is not available for this pair.

Δμwβ − I / L RT

=

Δμw0

−

RT0 +

∫T

T

Δhwβ − I / L

0

∫P

P Δv β − I / L w

RT

0

RT

2

Table 6. Absolute Average Deviation of the Hydrate Dissociation Temperature of Methane in the Presence of Thermodynamic Inhibitor

dT

dP − ln(a w )

inhibitor

(7)

∫T

T

ΔCP w dT

0

(8)

where14

i cal yz z(T − T0) ΔCP w = ΔCP0w − 0.0336jjj 2z k mol ·K {

(9)

Δh0w defines the difference between the enthalpy of the empty hydrate lattice and the ice phase at zero pressure. ΔC0Pw is the difference between the specific heat capacity of water in the empty hydrate lattice and ice or liquid water at 273.15 K and zero pressure. ΔCPw is the difference between the isobaric heat capacity of water between the empty hydrate lattice phase and ice or liquid water at any temperature or pressure. Note that Δh0w and Δvw are assumed to be pressure independent. The values of Δh0w, Δμ0w, and ΔC0Pw are given in Table 2. In this work, the water activity in the presence of alcohol or salt is calculated using the original UNIQUAC activity coefficient model modified by adding a Debye−Huckel term33 as follows in which GE is the excess Gibbs energy: E E E GE = Gcombinatorial + Gresidual + G Debye ‐ Huckel

P range, (kPa)

ref

AADa (K)

23 6 42 4 4 5 13 26 2 12 9 15 52 12 61

2390−11000 4230−8570 6600−7156 2592−13417 3778−13659 3580−9600 2710−8820 4920−10290 6570−7420 2810−9010 2140−18820 5000−62000 2142−50410 2420−16380 2504−9664

De Roo et al.37 Kharrat et al.38 Jager et al.39 Kobayashi et al.40 Kobayashi et al.40 Mohammadi et al.41 Mohammadi et al.41 Kharrat et al.38 Dalmazzone et al.42 Mohammadi et al.41 Ng et al.43 Blanc et al.44 Svartas et al.45 Robinson et al.46 Dholabhai et al.47

0.49 0.39 0.74 0.69 0.56 0.42 0.63 0.64 0.43 0.47 0.62 0.53 0.46 0.84 0.49

59 76 421

2050−16050 7470−68150

Jager et al.48 Jager et al.48

0.70 0.67 0.66

NaCl NaCl NaCl NaCl NaCl NaCl KCl CaCl2 CaCl2 CaCl2 MeOH MeOH MeOH EG NaCl+ KCl+ CaCl2 NaCl + MeOH NaCl + MeOH overall

in which aw is the activity of water. T0 and P0 are known as the reference temperature and pressure which are 273.15 K and the sublimation pressure at T0, respectively. Since P0 is small in value as compared to the hydrate equilibrium pressure, it is normally chosen to be zero. Δμ0w is the difference between the water chemical potential in empty hydrate lattice and the liquid phase at T0. Δvβ−I/L and Δhβ−I/L describe the molar volume w w difference and the molar enthalpy difference between the empty hydrate lattice phase and the liquid water/ice, respectively. Δhβ−I/L is defined as follows: w Δhwβ− I/L = Δhw0 +

no. of data

a

AAD =

1 NPTS

NPTS

∑i

|Tcal i − Texp | i

The combinatorial and residual terms are calculated as those of the original UNIQUAC activity coefficient model. The combinatorial term33 is calculated using the following equation: E Gcombinatorial = RT

i ϕi yz zz − z zz k xi { 2

∑ xi lnjjjjj i

i ϕi yz zz zz θ k i{

∑ qixi lnjjjjj i

(11)

where xi stands for the liquid mole fraction. T is the hydrate dissociation temperature and z demonstrates the coordination number which is considered to be 10. Volume fraction (ϕi) and surface area fraction (θi) of component i are as follows:

(10) C



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Table 7. Absolute Average Deviation of the Hydrate Dissociation Temperature of Ethane in the Presence of Thermodynamic Inhibitor no. of data

inhibitor NaCl NaCl KCl KCl CaCl2 CaCl2 NaCl + KCl NaCl + CaCl2 KCl + CaCl2 NaCl + KCl + CaCl2 MeOH MeOH MeOH EG EG EG overall a

AAD =

1 NPTS

P range, (kPa)

ref

AADa (K)

4 7 5 12 5 11 9 5 5 5

689−1524 540−2900 495−1577 470−2110 573−1613 440−2090 488−1851 519−1728 500−1454 558−1969

Tohidi et al.49 Mohammadi et al.41 Englezos et al.50 Mohammadi et al.41 Englezos et al.50 Mohammadi et al.41 Englezos et al.50 Englezos et al.50 Englezos et al.50 Englezos et al.50

0.49 0.30 0.71 0.20 0.15 0.70 0.38 0.16 0.76 0.32

12 15 35 8 6 9 157

3990−20400 417−2910 417−20400 510−2600 510−20130 1010−3400

Ng et al.43 Ng et al.43 Ng et al.43 Majumdar et al.52 Ng et al.43 Majumdar et al.52

0.23 0.46 0.46 0.47 0.75 0.67 0.44

NPTS

∑i

Table 9. Absolute Average Deviation of the Hydrate Dissociation Temperature of Hydrogen Sulfide in the Presence of Thermodynamic Inhibitor inhibitor

overall a

AAD =

ϕi =

θi =

AADa (K)

5 10 12 6 4 5 12 3 8 4 14

207−1448 290−1910 150−820 365−1565 332−432 1630−10350 140−1500 236−496 320−1500 189−777 329−1073

Bond et al.58 Mohammadi et al.64 Mohammadi et al.64 Bond et al.58 Mohammadi et al.65 Ng et al.43 Mohammadi et al.64 Mohammadi et al.60 Majumdar et al.52 Mohammadi et al.60 Mahadev et al.61

0.49 0.44 0.71 0.15 0.70 0.76 0.32 0.23 0.46 0.46 0.47

a

AAD =

1 NPTS

83 NPTS

∑i

P range, (kPa)

ref

inhibitor

200−531 179−455 221−421 180−460 234−427 234−427 157−372 234−441 181−432 133−471

Tohidi et al.49 Patil et al.53 Tohidi et al.49 Mohammadi et al.41 Englezos et al.54 Tohidi et al.49 Englezos et al.54 Tohidi et al.55 Englezos et al.54 Bishnoi et al.56

0.49 0.30 0.71 0.20 0.15 0.70 0.38 0.16 0.76 0.32

3 17 4

1720−6510 228−6510 215−426

Ng et al.43 Ng et al.43 Mahmoodaghdam et al.57

0.23 0.46 0.47

NPTS ∑i |Tcal i

NaCl NaCl NaCl NaCl KCl KCl CaCl2 CaCl2 CaCl2 NaCl + KCl NaCl + KCl NaCl + CaCl2 NaCl + MeOH MeOH NaCl + KCl+ MeOH EG EG EG overall

AADa (K)

19 8 15 4 5 14 5 9 7 53

0.42

a

i

(12)

AAD =

1 NPTS

no. of data

P range, (kPa)

ref

AADa (K)

25 57 57 4 21 4 17 21 4 17 12 22 3 4 30

1162−3907 2628−4384 1189−4226 200−400 1130−3905 480−2000 960−3824 960−3824 2100−3600 1218−3976 1517−3613 1042−3697 1223−2512 1012−2560 910−3038

Dholabhai et al.62 Vlahakis et al.63 Vlahakis et al.63 Mohammadi et al.41 Dholabhai et al.62 Mohammadi et al.41 Tohidi et al.55 Dholabhai et al.62 Mohammadi et al.41 Tohidi et al.55 Dholabhai et al.62 Dholabhai et al.62 Mohammadi et al.60 Mohammadi et al.60 Mahadev et al.61

0.19 0.40 0.10 0.12 0.30 0.38 0.29 0.66 0.46 0.37 0.27 0.42 0.28 0.57 0.45

6 4 8 316

470−20640 1150−3200 1060−3140 -

Ng et al.43 Fan et al.66 Majumdar et al.52

0.64 0.55 0.61 0.36

NPTS

∑i


uki = uki0 + ukit(T − 298.15)

(13)

(15)

(16)

The interaction energy parameters are reported in Table 4 and Table 5.33−36 The Debye−Huckel term is calculated using the following equation:33 ÄÅ ÉÑ E G Debye 4A ÅÅÅ b′2 I ÑÑÑ − Huckel 1/2 1/2 Å ÑÑ = − x wM w 3 ÅÅln(1 + b′I ) − b′I + RT 2 ÑÑÑÖ b′ ÅÅÇ

The volume (r) and surface area (q) parameters of component i33−36 are given in Table 3. The residual term33 is defined as follows: E ij yz Gresidual = −∑ xiqi lnjjjj∑ θkψki zzzz j k z RT i k {

i

where uki and uii stand for the interaction energy parameters which are assumed to be temperature dependent in this study:

xiqi ∑l xlql

|Tcal i − Texp |

i u − uii yz zz ψki = expjjj− ki T { k

− Texp |

xiri ∑l xlrl

0.51

Table 10. Absolute Average Deviation of the Hydrate Dissociation Temperature of Carbon Dioxide in the Presence of the Thermodynamic Inhibitor

i

163 1 NPTS

ref

|Tcal i − Texp |

no. of data

NaCl NaCl KCl KCl CaCl2 CaCl2 NaCl + KCl NaCl + CaCl2 KCl + CaCl2 NaCl + KCl + CaCl2 MeOH MeOH EG

P range, (kPa)

NaCl NaCl KCl CaCl2 CaCl2 MeOH MeOH MeOH EG NaCl + MeOH NaCl + KCl + MeOH overall

Table 8. Absolute Average Deviation of the Hydrate Dissociation Temperature of Propane in the Presence of Thermodynamic Inhibitor inhibitor

no. of data

(14)

(17) D


ÄÅ ÅÅ ÅÅ ln i y ϕ Å z j z ln(γiC) = lnjjj i zzz + 1 − qiÅÅÅÅ j xi z 2 ÅÅÅ k { ÅÅ ÅÇ ÄÅ ÅÅ ji zy Å ln(γi R ) = qiÅÅÅÅ1 − lnjjjj∑ θkψki zzzz − j k z ÅÅ ÅÇ k {

ÉÑ ÑÑ Ñ + 1 − ϕ iÑ ÑÑ θi ÑÑ ÑÑ θi ÑÑ ÑÑ (20) ÑÖ ÉÑ θ ψ ÑÑÑ ∑ k kl ÑÑÑÑÑ ∑l θlψlk ÑÑ k (21) Ö Partial molar differentiation of eq 17 gives the activity coefficient of water related to the Debye−Huckel part:

Journal of Chemical & Engineering Data Table 11. Absolute Average Deviation of the Hydrate Dissociation Temperature of Mixtures of Methane + Carbon Dioxide in the Presence of Thermodynamic Inhibitors inhibitor NaCl NaCl NaCl + KCl+ CaCl2 MeOH MeOH EG EG EG NaCl + KCl + MeOH NaCl + KCl + MeOH overall a

AAD =

1 NPTS

no. of data

P range, (kPa)

ref

AADa (K)

13 7 77

3592−3592 1100−4800 1830−9150

Elliot et al.67 Fan et al.68 Dholabhai et al.69

0.64 0.69 0.45

20 15 3 14 6 5

1490−19010 2211−9676 1920−9167 930−3220 2420−15240 2063−9682

Ng et al.70 Dholabhai et Dholabhai et Fan et al.66 Dholabhai et Dholabhai et

al.71 al.71

0.60 0.29 0.83 0.67 0.36 0.67

3

2172−9705

Dholabhai et al.71

0.46

al.71 al.71

172 NPTS

∑i

Article

ϕi

()

ln(γi D ‐ H) = M w

Ä ÑÉÑ 2A ÅÅÅÅ 1 1/2 1/2 Ñ ÑÑ Å bI bI 1 + − − 2 ln(1 + ) Å ÑÑ ÑÖ b3 ÅÅÇ 1 + bI1/2 (22)

The summation of eq 20−22 gives the activity coefficient of water: ln(γw ) = ln(γwC) + ln(γwR ) + ln(γwD ‐ H)

(23)

0.52

3. RESULTS AND DISCUSSION The predicted hydrate dissociation temperatures of systems containing methane, ethane, propane, hydrogen sulfide, and carbon dioxide in the presence of different thermodynamic inhibitors such as NaCl, KCl, CaCl2, MeOH, EG, and their mixtures are given in Tables 6 to 10. And also, the predicted hydrate dissociation temperatures for systems containing mixtures of hydrate formers in the presence of pure water and mixtures of thermodynamic inhibitors are reported in Table 11 and 12. The experimental data and the model results are compared in Figures 1−12. There is a reasonable agreement between the compared values. Figures 1−5 show the hydrate dissociation temperature for methane (419 data points), ethane (157 data points), propane (163 data points), hydrogen sulfide (83 data points), and carbon dioxide (316 data points) in the presence of a single or mixtures of inhibitors (NaCl, KCl, CaCl2, MeOH, and EG), respectively. Average absolute deviation (AAD) for the studying systems reported in Tables 6−10 confirm the accuracy of the proposed model. Note that, the effect of high solubility of CO2 and H2S in the liquid phase is considered in the current model while the molecular interaction between these two gases and other components in the liquid phase is neglected. Comparing the


1

where I stands for the ionic strength (I = 2 ∑i mizi2 , m defines the molality and z is the ion charge), xw and Mw are mole fraction and molecular weight of water, respectively. b is a constant equal to 1.5 (kg mol−1)1/2 and A represents the Debye−Huckel parameter calculated as33 ÅÄ ÑÉÑ1/2 ÑÑ F 3 ÅÅÅÅ d ÑÑ A= Å 4πNA ÅÅÅÅÇ 2(ε0εrRT )3 ÑÑÑÑÖ (18) where F is the Faraday’s number, NA represents the Avogadro’s number, and ε0 demonstrates the vacuum permittivity. εr and d are temperature-dependent parameters that are known as relative permittivity and density of water, respectively. To calculate the Debye−Huckel parameter in a temperature range of 273.15 to 383.15 K, the following equation is used: A = [1.131 + 1.335.10−3(T − 273.15) + 1.164.10−5 × (T − 273.15)2 ]

(19)

Partial molar differentiation of eqs 11 and 14 results in the combinatorial, ln(γCi ), and the residual terms ln(γRi ), as follows:33

Table 12. Absolute Average Deviation of the Hydrate Dissociation Temperatures of Different Mixtures of Methane, Ethane, Propane, Carbon Dioxide, and Nitrogen in the Presence of Different Thermodynamic Inhibitors gas mixturea methane + ethane methane + ethane overall methane + propane + carbon dioxide methane + propane + carbon dioxide methane + propane + carbon dioxide overall methane + nitrogen methane + nitrogen overall methane + propane ethane + carbon dioxide carbon dioxide + nitrogen overall

inhibitor

no. of data

NaCl methanol

29 13 42 5 6 12 23 8 8 16 8 4 7 11

NaCl methanol NaCl + CaCl2+ MeOH NaCl NaCl methanol NaCl NaCl

a

P range (kPa)

72

2300−12600 1400−19020

Maekawa et al. Ng and Robinson70

2876−9849 2567−8942 2672−9744

Bishnoi et al.73 Bishnoi et al.73 Bishnoi et al.73

3080−12680 4330−11410

Mei et al.74 Mei et al.74

903−13831 1170−3900 1120−3160

Ng et al.70 Fan et al.68 Fan et al.68

Since there are too many different mixtures, the compositions are not mentioned here. bAAD = E

AADb (K)

ref

1 NPTS

NPTS

∑i

0.59 0.55 0.58 0.34 0.33 0.44 0.39 0.56 0.23 0.39 0.87 0.19 0.38 0.46




Article

Figure 1. Experimental36,48 and calculated values of hydrate dissociation temperature of methane. No. of data points: 419.

Figure 4. Experimental53,59,62 and calculated values of hydrate dissociation temperature of hydrogen sulfide. No. of data points: 83.

Figure 2. Experimental41,43,49,53 and calculated values of hydrate dissociation temperature of ethane. No. of data points: 157.

Figure 5. Experimental43,53,56,63,67 and calculated values of hydrate dissociation temperature of carbon dioxide. No. of data points: 316.

It should be noted that the larger errors for temperatures below 273 K in Figure 3 is due to applying eq 19 beyond its validity range. Figures 6 and 7 show the hydrate dissociation temperature for methane+carbon dioxide and methane+ethane in the presence of single or mixed inhibitors, respectively. Figures 8−12 depict the hydrate dissociation temperature for mixtures of CO2+CH4+ C3H8, N2+ CH4, CH4+C3H8, C2H6+CO2 and CO2+N2 when single or mixed inhibitors are present. The AAD of the prediction results given in Tables 11 and 12 confirms the reliability of the proposed model. The results show that the overall AAD is about 0.50 K. The deviation may be resulted from the uncertainty of the experiments, ignoring some interactions between the dissolved gases and the present ions in the liquid phase or the uncertainty of some estimated interaction parameters. The comparison between the predicted results and the results obtained from the models published by Nasrifar et al.21 and Javanmardi et al.22 is shown in Tables 13−16. The modeling results confirm the accuracy of the current model, rather than two other models especially when both kinds of thermodynamic inhibitors (electrolyte and alcohol) are present. For example, Table 14 shows that the AAD of

Figure 3. Experimental41,43,49,50,54,58 and calculated values of hydrate dissociation temperature of propane. No. of data points: 163.

predicted results with the experimental data confirms this assumption. Some ternary and tertiary gas mixtures were also investigated to check the capability of the extended UNIQUAC activity coefficient model for the gas mixtures. F



Article

Figure 6. Experimental67,72 and calculated values of hydrate dissociation temperature of mixture of methane and carbon dioxide. No. of data points: 172.

Figure 9. Experimental75 and calculated values of hydrate dissociation temperature of mixture of methane and nitrogen. No. of data points: 16.

Figure 10. Experimental71 and calculated values of hydrate dissociation temperature of mixture of methane and propane. No. of data points: 8.

71,73

Figure 7. Experimental and calculated values of hydrate dissociation temperature of mixture of methane and ethane. No. of data points: 124.

Figure 11. Experimental69 and calculated values of hydrate dissociation temperature of mixture of ethane and carbon dioxide.

Figure 8. Experimental74 and calculated values of hydrate dissociation temperature of mixture of methane, propane, and carbon dioxide. No. of data points: 23.

for the gas mixture of 50% CH4 + 50% CO2 in the presence of 15% NaCl + 5% MeOH. This better prediction is a result of the better prediction of water activity using the extended UNIQUAC in comparison of those used by previous researchers.

Nasrifar et al.21 and Javanmardi et al.22 models are 1.94 and 1.42 K, respectively, while the AAD of the current work is 0.40 K G



Article

Table 15. Absolute Average Deviation of the Hydrate Dissociation Temperature of a Gas Mixture73 (78% CH4 + 20% CO2 + 2% C3H8) in the Presence of Pure Water or Single or Mixed Inhibitors AAD (K)

Figure 12. Experimental69 and calculated values of hydrate dissociation temperature of mixture of carbon dioxide and nitrogen.

pure water Na10 K10 Ca10 Na2K0.5Ca0.5 Me10 Me20 K10Me10 Na10Me10 Na20Me10 K10Me20 overall

8 8 6 7 6 7 7 7 7 6 6 75

P range (kPa) 920−2670 810−3430 780−2810 630−3340 600−2750 610−2710 740−4500 1050−4900 1600−3200 1700−4960 1800−11180

Nasrifar et al.21

Javanmardi et al.22

this work

0.78 1.35 0.92 1.46 0.62 2.40 0.66 0.58 3.43 3.11 1.60

0.53 0.34 0.96 0.36 0.60 1.80 0.67 0.63 1.10 4.29 2.96 1.18

0.87 0.35 0.62 0.58 0.99 1.75 0.67 0.35 0.49 0.47 0.37 0.68

P range (kPa)

Nasrifar et al.21

Javanmardi et al.22

this work

pure water Na5 Na10 Na20 Me10 Me20 Na5Me5 Na10Me10 Na5Me15 overall

4 3 2 3 3 3 3 6 3 30

1660−7241 3269−9849 2876−5633 3728−8874 2567−8846 3189−8942 2672−8490 3853−9744 3443−8250

− 0.60 1.19 4.94 1.74 2.59 1.79 3.33 2.22 2.46

0.47 0.48 0.14 1.78 0.47 0.40 0.47 0.73 1.20 0.70

0.39 0.39 0.26 1.61 0.34 0.32 0.32 0.53 0.42 0.52

AAD (K)

AAD (K) no. of data

no. of data

Table 16. Absolute Average Deviation of the Hydrate Dissociation Temperature of Gas (a) H2S, (b) CO2 or (c) C2H6 in the Presence of Single or Mixed Inhibitor52

Table 13. Absolute Average Deviation of the Hydrate Dissociation Temperature of a Gas Mixture75 (97.25% CH4 + 1.42% C2H6 + 1.08% C3H8 + 0.25% i-C4) in the Presence of Pure Water or Single or Mixed Inhibitors

aqueous phasea

aqueous phase

aqueous phase

gas type

P range (kPa)

Nasrifar et al.21

Javanmardi et al.22

this work

Eg30 Eg15 Na10Eg15 Eg15 Eg30 Na10Eg15 Na10Eg10 Na15Eg10 Eg15 Eg30 overall

a a a b b b b b c c

5 5 5 5 3 3 5 4 5 4 44

230−1500 220−1440 270−1460 1060−3140 1200−2650 1660−2890 1390−3180 1830−2670 510−2600 710−2380

0.40 0.61 0.57 0.81 0.36 0.38 0.27 0.95 0.42 0.40 0.52

0.19 0.08 0.98 0.31 0.43 0.45 0.48 0.48 0.48 0.63 0.45

single or mixed inhibitors are present. For this purpose, the extended UNIQUAC activity coefficient model incorporated with the Debye−Huckel term is applied. The hydrate former gases studied in this work are CH4, C2H6, C3H8, N2, H2S, CO2, and their mixtures. The investigated thermodynamic inhibitors include NaCl, KCl, and CaCl2 as well as their mixtures, ethylene glycol, and methanol, and mixtures containing salts and alcohol. The mean AAD value of about 0.50 K is obtained

a

Na, K, Ca, Me, and Eg, stand for NaCl, KCl, CaCl2, methanol, and ethylene glycol, respectively. As an example Na2K0.5Ca0.5 is a system of 2% NaCl, 0.5% KCl, and 0.5% CaCl2.

4. CONCLUSION In the current study, the activity coefficient based model was used to predict the hydrate dissociation temperature when

Table 14. Absolute Average Deviation of the Hydrate Dissociation Temperature of a Gas Mixture71 ((a) 50% CH4 + 50% CO2 or (b) 80% CH4 + 20% CO2) in the Presence of Single or Mixed Inhibitors AAD (K) aqueous phase

gas type

no. of data

P range, (kPa)

Nasrifar et al.21

Javanmardi et al.22

this work

Na5Me15 Na10Me10 Me20 Me10 Me20 Na5Me5 Na15Me5 K10Me5 Na19Me10 Eg10 Eg30 overall

a a a a b b b b b b b

3 3 3 6 6 3 3 3 3 3 3 39

2564−6888 2153−6785 1877−6731 2627−8022 2376−9676 2140−9682 2151−9371 2172−9705 2063−8754 1920−6318 2428−9167

0.34 1.17 1.77 1.10 1.38 0.73 1.94 1.42 1.42 1.00 0.89 1.60

2.02 1.46 0.46 0.10 0.15 0.74 1.42 0.11 1.30 0.66 0.84 1.18

1.18 0.57 0.33 0.30 0.27 0.76 0.40 0.47 0.48 0.05 0.68 0.51

H



Article

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for 1455 data points containing pure hydrate formers or mixtures of the above-mentioned gases. Results confirm the accuracy of the current model while thermodynamic inhibitors are present in the system. The results obtained from this model for some systems have been compared with two other existing thermodynamic models. It was observed that the present model is more accurate than the other models.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Jafar Javanmardi: 0000-0002-4146-1490 Amir H. Mohammadi: 0000-0002-2947-1135 Present Address ⧫

National Iranian Oil Products Distribution Company, Fars, Abadeh, Iran.

Notes

The authors declare no competing financial interest.

■

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K


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