Pressure / MPa

Measurements and Predictions of Phase Equilibria for Water + Ethane in Hydrate-Forming Conditions

Y. S. Kim¹, S. O. Yang¹, S. S. Kim², C. S. Lee¹

1) Chemical and Biological Engineering, Korea University

2) Environment Technology Department, Suwon Science College

Introduction

 Gas Hydrate (Clathrate Hydrate)

 a solid solution of water and light gases through hydrogen bonding

 Researches on the gas hydrate

 Methane hydrates as a future resource of energy

 Carbon dioxide sequestration as hydrates in deep ocean

 Process problems in petroleum industry

• Effects of inhibitors on hydrate-forming condition

• Prediction of phase equilibria for mixed hydrates

What are gas hydrates ?

 Crystalline solids consisting of a guest(s) component(s) and water

 Hydrates can form at conditions above the normal freezing point of water by the hydorogen bonding.

 Three cavities in gas hydrates

(a) Pentagonal Dodecahedron(5¹²) (b)Tetrakaidecahedron(5¹²6²) (c)Hexakaidecahedron(5¹²6⁴) (Reproduced from “Clathrate Hydrates of Natural Gases”, Sloan, 1998)

 Structures of gas hydrates

 Structure I(a) and II(b) form with relatively small guests, e.q., methane, ethane, nitrogene, etc.

 Structure I and II contains 48 and 136 water molecules, respectively.

 Structure H(c) is only known to form with at least one small guest (i.e., methane) and one large guest, e.q., cyclooctane, methylcylcohexane, etc.

Studies on Ethane Hydrate

 H-L_W-V_C2H4 and H-I-V_C2H4

 Roberts et al.(1940) …

 H-L_W-L_C2H4

 Ng and Robinson(1985)

 H- П_C2H4

 Sloan(1986)

 Song and Kobayashi(1994)

Figure 1. Phase diagram of H2O - C2H6

Temperature / K

260 270 280 290

Pressure / MPa

0.1 1 10

H-I or H-Lc H-Lw or H-Lc

Lw-Lc

H-Lw or H-V

Lw-Lc I-V

H-V or H-I Q2(H-Lw-Lc-V)

Q1(H-I-L-V) H-I-V

H-L-V H-Lw-Lc

Models on Gas Hydrate

 Van der Waals and Platteeuw [1959]

 Statistical model of hydrate cavities similar to gas adsorption model by Langmuir

 Holder et al.[1980]

 The chemical potential difference between the hypothetical empty hydrate and the fluid phase or ice is calculated by classical

thermodynamic relations

 Klauda and Sandler(2000)

 Fitting the vapor pressure of the empty hydrate for each guest component

Purpose

 Experimental determination of H-L_W equilibria

 Effect on ethane solubility by existence of NaCl

 EOS approach available on

 three-phase equilibria (H-I-V_C2H6, H-L_W-V_C2H6 , H-L_W-L_C2H6 )

 two-phase equilibria (H-L_W , H-L/V_C2H6)

 Applicability of Nonramdom Lattice Fluid Thoery (NLF-HB) and Gibbs energy model on hydrate containing equilibria

NLF-HB Equation of State

 Nonrandom Lattice Fluid Hydrogen Bonding Theory

 NLF EOS by You et al. [1993 a, b]

 Expansion to associating system using Veytsman statistics[1990]

by Yeom et al. [1999]

 A normalization of Veytsman statistics by Lee et al. [2000]

 Parameters for pure species

 Hydrogen-bonding energy and entropy for H₂O-H₂O interaction

 E_HB⁰ = –15.5 kJ/mol, S_HB⁰ = –16.5 J/mol-K by Luck [1980]

)]

15 . 273 T

( ) T / 15 . 273 ln(

T [ ) 15 . 273 T

( k

/ _{a b c}

ii =ε +ε − +ε + −

ε

)]

15 . 273 T

( ) T / 15 . 273 ln(

T [ r ) 15 . 273 T

( r r

r_i = _a + _b − + _c + −

NLF-HB Equation of State

 Expression for Pressure

 Expression for chemical potential



= 2 i j ij

M (1/θ ) θθ ε

ε +⁽β ^/2θ2 ⁾θiθjθkθlεij⁽εij +εkl −εik −ε jk ⁾

) r N N

/(

r

N_{i i 0} ^C_{i 1 i i}

i ^{= +}₌

ρ ^θi ^{= N}i^qi ^/(N0 ⁺^C_i=1^Ni^qi ⁾



 _{= =}  _{= =} ^_^ ₌



 −

= ^C_{i 1} i i

K 1 k

L 1 l

K 1 k

L 1 l

0 klHB klHB

HB N N / N r

ν









 +



 

 + 

−

−



 



 



 



 −

+ +



 



− 

− =

2 q z ln q

) 1 ln(

r r 1

1 q ln RT r

ln V RT

M 2 i i

i i M

i M 0 H

i

i μ ρ ρ θ β ε θ

μ^{Π Π}

 

 

= =

+

+









 + + − −

−

−

× ^m

1 k

n

1

k HB0

k 0

HBk i 0

0 k HB0 k

HB0 i k

2 k M

ik jk kl

ij ij l k j ik

k i

i

N ln N N a

ln N ) d

2 2

( 2

q 1 r

θ ε

ε ε ε

ε ε θ θ θ β

ε θ



 



 



 



−











 − − −



 







 



 −

+



 



= 

H 2 M HB

M M

H 2 V

) z 1 ln(

r 1 1 q 2 ln z V

P 1 ρ ρ ν ρ θ ε

β

Thermodynamic Model for Hydrate Phase Equilibria

 Hydrate phase by van der Waals and Platteeuw model(1959)

)]

f C 1 /(

f C 1 ln[

RT _{j j i,j i i,j i}

WEH

WH μ ν Π Π

μ = +  − +

] RT / ) exp[(

P

f_i^Π = ⁰ μ_i^Π −μ_i^Π0 dr kT r

) r ( exp W

kT

C 4 ^R

0

ki ^{= π}  ^_^{− }_^ 2

 Chemical potential difference between empty hydrate and reference fluid state

dP ) RT / V ( dT

) RT / H ( )

P , T

( ^P

P

WH T 2

T

WH 0

0 0 EH W

W

0

0 

 ⁺

+

=μ^Π Δ ^Π Δ ^Π

μ

] f

/ f

ln[

RT _pure^EH_{W pureW}

W 0

WEH μΠ Π

μ = +

] P P [ V ]

P / P

ln[

RT _W^EH _W^EH _{pureW W}^EH _W^EH

W 0 + + −

= μ^Π φ ϕ^Π Δ

Chemical Equility

 Three-phase equilibria

W 0 WH

W 0

WΠ μΠ μ μΠ

μ − = −

) 2 i ( ) 1

iΠ( μΠ

μ =

)]

f C 1 /(

f C 1 ln[

RT _{j j i,j i i,j i}

W 0

WH μΠ ν Π Π

μ − =  − +

] [

] /

ln[P_W^EH _W^EH P _pureW V_W^EH P P_W^EH

RT +Δ −

+ φ ϕ^Π

 Two-phase equilibria

W 0 WH

W 0

WΠ μΠ μ μΠ

μ − = −

 Phase equilibria for containing electrolyte

iE LEoS

L i

i = μ _, + RT lna μ

Pure parameters for NLF-HB EOS

 Pure parameter regression

 Vapor pressure and saturated liquid & vapor density

Table 1. Pure parameters for NLF-HB EOS

)]

15 . 273 T

( ) T / 15 . 273 ln(

T [ ) 15 . 273 T

( k

/ _{a b c}

ii =ε +ε − +ε + −

ε

)]

15 . 273 T

( ) T / 15 . 273 ln(

T [ r ) 15 . 273 T

( r r

r_i = _a + _b − + _c + −

ε^a ε^b ε^{c ra rb×103 r×103c}

H2O 134.022 7.8×10^-5 -0.229 1.727 -0.002 -3.749 C₂H₆ 76.378 -4.9×10^-7 -0.110 5.091 -0.007 10.384

 Hydrogen-bonding parameters for H₂O-H₂O interaction

mol kJ

E_HB⁰ =−17.95 / S_HB⁰ =−16.6 kJ /mol

Gibbs Energy Model(Lee et al., 1996)

 Pure parameter

 Solvent or non-ionic molecule : 2 parameters

 Ion : 3 parameters

Components r_s,j[Å] r_j[Å] ε_ii[kJ/mol]

Water - 2.500 2.062

Ethane - 6.3056 0.1733

Na⁺ 2.327 2.554 5.521

Cl⁺ 3.017 0.484 1.362

 H₂O – C₂H₆ interaction parameter

k_ij=0.6276-187.123/T[K]

Experimental Apparatus

 System accuracy

 Pressure : ±0.06 MPa

 Temp. : ±0.05 K

 Mole fraction : 5.3%

 Reproducibility of syringe pump : 0.5%

Figure 2. The experimental apparatus for measurement of the equilibrium pressure and the solubility of dissolved gas in the hydrate containing equilibria

(1)vacuum pump; (2)magnetic stirrer; (3)sampling cell; (4)sampling valve; (5)sampling loop;

V

-L

equilibria

 Binary parameter for C₂H₆-H₂O

k_ij= 0.90994-195.56/T

Table 2. Calculated L_W-V_C2H6 equilibrium composition

a) Mole fraction of ethane in water rich phase

Figure 3. Isothermal vapor-liquid equilibria for water +ethane system at 298.15 K

Mole fraction of ethane

0.000 0.001 0.002 0.997 0.998 0.999 1.000

Pressure / bar

0 20 40 60 80

Present Measurements Data by Coan et al. [1971]

Regressed data by Song and Kobayashi[1994]

Present calculation

Present measurements(NaCl 1.0 M) Present calculation(NaCl 1.0 M)

NaCl pts AADx [%]

P range

[bar] Type

0 8 4.3 13.7-35.4 a

0 4 11.0 24.4-36.1 b

1 M 3 26.7 32.2-57.4 a

b) Mole fraction of watee in ethane rich phase

Three-phase equilibria

Table 5. Comparison of calculated 3-phase equilibrium pressure

Phase pts Calculated error ^a) Present Sloan Klauda

H-I-VC2H6 7 2.8 6.8 4.0

H-LW-VC2H6 61 2.6 9.0 5.2 H-L_W-L_C2H6 17 15.4 35.8 -

Table 4. Kihara potential for ethane hydrate

ε/k [K] σ[Å] a^a)[Å]

C₂H₆ 144.7597 3.2606 0.5651 a) Radius of the spherical core(a) was from

Sloan(1998)

Figure 4. Comparison of experimental and calculated

Temperature / Kelvin

255 260 265 270 275 280 285 290 295

Pressure / MPa

1 10

Robert (1940)

Deaton and Frost (1946) Reamer(1952)

Galloway(1970) Holder(1980)

Ng and Robinson(1985) Avlontis(1988)

Klauda and Sandler(2000) Sloan(1998)

Present calculation Present calculation (NaCl 1.0M)

H-П

Equilibria

Figure 5. Comparison of calculated water contents in ethane- rich phase of H-L/VC2H6 equilibria with data of Sloan et al.

(1986) and Song and Kobayashi (1994)

Temperature / K

250 260 270 280 290 300

Water content / ppm

10 100 1000

Data of Song and Kobayashi at 2.48 MPa(1994)

Data of Song and Kobayashi at 3.45 MPa(1994)

Data of Sloan at 3.45 MPa(1986) Present calculation at 2.48 MPa Present calculation at 3.45 MPa

Table 6. Comparison of calculated Water content in ethane rich phase

Phase pts Sloan^a)

[%]

Present^a) [%]

H-VC2H6b) 3 69.3 21.6 H-L_C2H6^b) 4 14.0 16.1 H-LC2H6c) 6 16.6 29.2 a) absolute Average Deviation in mole fraction b) Song and Kobayashi(1994)

c) Sloan et al.(1986)

H-Lw equilibria

Temperature / K

270 275 280 285

Pressure / bar

0 50 100 150 200

Experimental data at x = 0.0004115

Experimental data at x = 0.0004677(NaCl 1 M) Present calculation at x = 0.0004115

Present calculation at x = 0.0004115(NaCl 1 M) Present calculation at x = 0.0004677

Present calculation at x = 0.0004677(NaCl 1 M)

Table 7. Comparison of calculated Ethane solubility in water phase

NaCl pts AAD^a)[K]

0 3 0.09

1 M 3 4.84

a) Absolute Average Deviation in temperature(K)

Figure 7. Comparison of calculated isobaric solubility of ethane in liquid water phase of H-Lw equilibria with experiments at 100 bar

274 276 278 280 282

mole fraction of ethane in water

0.0002 0.0004 0.0006 0.0008 0.0010 0.0012

Present calculation at 100 bar

Present calculation at 100 bar (NaCl 1 M) Present calculation at 150 bar

Present calculation at 150 bar(NaCl 1 M) Present measurement at 100 bar

Present measurement at 100 bar (NaCl 1 M)

Temperature / K

Conclusion

 H-Lw Equilibrium compositions of ethane were experimentally determined.

 Recently proposed NLF-HB EOS was applied to various hydrate-containing phase equilibria.

 Effects of salt on hydrate-containing phase equilibria were experimentally determined for H-Lw equilibria and predicted for three-phase (H-I-V_C2H6 , H-L_W-V_C2H6, H-L_W-L_C2H6 ) and two-phase (^H-L_W ) equilibria.