1

LW-H Equilibrium Measurements andUnified Predictions of Hydrate-Containing

Phase Equilibriafor Methane, Ethane, Propaneand Their Mixtures

S. O. Yang, Y. S. Kim, S. K. Ryu and C. S. Lee

Thermodynamics and Properties LaboratoryDept. of Chemical Engineering, Korea University

2

Motivation

The methane hydrate as a possible energy resource or the CO2hydrate as a deep-ocean sequestration Necessity for reliable solubility data in water-rich phase of

hydrate-containing systems (H-LW). Measurement of solubility using indirect method for sparingly

soluble gas components.

Necessity for comprehensive calculation methods Unified method to the hydrate-containing systems The applicability of Nonrandom lattice fluid hydrogen bonding

theory (You et al. 1994a, 1994b; Lee et al., 2001)

3

Computation of Hydrate Phase Equilibria

Equality of Chemical potential(or fugacity)

where α or β denotes V, LW, LC or Ice phase.

is obtained from EOS and from vapor pressure and saturated molar volume(Sloan et al., 1976)

• H-LW-V, H-I-V, H-LW-LC : Yang et al.(2000), Present work (Mixture)• H-LW-V, H-I-V : Klauda and Sandler (2000)• H-Lc, H-V, H-LW : Yang et al.(2000, 2001), Present work (Mixture)• H-Lc, H-V : Sloan(1976)

( ) ( ) or EHii

EHii

EHi

Hiii

Hi μμμμμμμμμ βαβα −=−=−==

( )βαii

Hi fff ==

βαμ or i

IceW

EHW μμ and

4

Computation of Hydrate Phase Equilibria

is obtained from(Holder et al.,1980)

• H-LW-V, H-I-V : Holder et al.(1980), Sloan (1998)• H-V, H-LC : Anderson and Prausnitz(1986), Munck et al.(1988)

is obtained from the statistical model by van der Waals and Platteeuw (1959).

EHWW μμ βα −or )( and ),(),,( 00 PVTHPT EH

WEH

WEHW ΔΔΔμ

wwPP

EHWT

T

EHWoo

EHWW

EHW xdP

RTVdT

RTH

RTPT

RT ooγμμμ ln),(

2 −Δ+Δ−Δ=−

Π

EHW

HW μμ −

Π+−= j jmjm mEHW

HW fCRT ]1ln[ ,νμμ

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Chemical Potential in Fluid Phase

Nonrandom Lattice Fluid Hydrogen Bonding Theory NLF EOS by You et al. [1994 a, b] Expansion to associating system using Veytsman statistics[1990]

by Yeom et al. [1999] A normalization of Veytsman statistics by Lee et al. [2001]

Parameters for NLF-HB theory Pure species : energy and size parameters Hydrogen-bonding energy and entropy for H2O-H2O interaction Binary interaction parameter for interactions between molecules

6

Chemical Potential of Water in Hydrate Phase

Statistical model by van der Waals and Platteeuw(1959)

is the fugacity of a component j in the equilibrium fluid phase.

Cj,m is the Langmuir constants.

• Calculated from the Kihara potential function • Kihara potential parameters are fitted from the three-phase

equilibrium pressure for each guest species.

Π+−= j jmjm mEHW

HW fCRT ]1ln[ ,νμμ

]/)exp[( 00 RTPf jjj μμ −= ΠΠ

drrkT

rWkT

TCiR

mj

−=

0

2,

)(exp4)( π

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Chemical Potential of Empty Hydrate

φWsatEH of the empty hydrate is assumed to be unity.

Vapor pressure of empty hydrates• Fitted to equilibrium pressures of multi-guest and simple hydrates• Structure I :

• Structure II :

Molar volume of empty hydrates• Correlated equation regressed by Avlonitis (1994)•

( ) ( )satEHW

satEHW

satEHW

satEHWW

EHW PPVPRT −++= φμμ ln0

TatmP EHsatW /25.6072410.17]/ln[ −=

TatmP EHsatW /34.6121515.17]/ln[ −=

])()()(1[ 303

202010 TTkTTkTTkVV satEH

W −+−+−+=

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Chemical Potential of Ice

If saturated vapor pressure and molar volume of ice are known

Fugacity coefficient of ice,φWsatI is assumed to be unity.

Saturated vapor pressure is obtained from subcooled water properties(Perry et al., 1989)

Molar volume of ice use the correlation equation regressed by Avlonitis (1994)

( ) ( )satIW

satIW

satIW

satIWW

IW PPVPRT −++= φμμ ln0

5171.537.64159247.17]/ln[

+−=

TbarPsatI

W

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Experiments

Direct method for small gas solubility Applicable to salt-containing systems Measurements by expansion of a liquid sample Mole fraction of gas calculated by pressure changes in expansion

chamber

• Yang, S. O., Yang, I. M., Kim, Y. S. and Lee, C. S., “Measurementand prediction of phase equilibria for water+CO2 in hydrate formingconditions”, Fluid Phase Equilib., 175 (2000), 79-85

• Yang, S. O., Cho, S. H., Lee, H. and Lee, C. S., “Measurement andprediction of phase equilibria for water+methane in hydrate formingconditions”, Fluid Phase Equilib., 185 (2001), 53-63

Not applicable to very sparingly soluble hydrocarbons

10

Experiments

Indirect method for very small gas solubility With known composition of liquid phase, the phase transition

point is detected by visual inspection.

• Rumph, B. and Maurer, G., “An Experimental and Theoretical Investigation on the solubility of Carbon Dioxide in Aqueous Solutions of Strong Electrolytes”, Ber. Bunsenges. Phys. Chems., 97(1993), 85-97

Present study for water + methane or ethane in hydrate-forming conditions

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Experimental Apparatus

3

2

6

7

5

PPT

T

8

9

14

11

1P

12

10

1315

4

2

Figure 1. The experimental apparatus for measurement of the equilibrium pressure and thesolubility of dissolved gas in the hydrate containing equilibria(1)vacuum pump; (2)magnetic stirrer; (3)sampling cell; (4)sampling valve; (5)sampling loop;(6)metering pump; (7)density transducer; (8)water bath; (9)equilibrium cell; (10)flask;(11)syringe pump; (12)line filter; (13)gas bomb; (14) pressure gauge (15) McHugh typevariable volume view cell

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The Reliability of the Experimental Procedure

Comparison between present methane solubility in water and those of DECEHEMA series

The accuracy in mole fraction Present work : 4.8 % AAD DECHEMA : 5.3 % AAD

Pressure / MPa

0 5 10 15 20

XC

H4

0.0001

0.001

0.01

Yarym-Agaev et al. [1983]Culverson and Mcketta [1951]Yokoyama et al. [1988]Wang et al.[1995]Deffy et al. [1961]CalculatedPreasent Work

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Three Phase Equilibria for Methane Hydrates

Temperature / K

260 265 270 275 280 285 290 295

Pres

sure

/ M

Pa

1

10

100

Data of Deaton and Frost (1946)Data of McLeod and Campbell (1961) Data of Jhaveri and Robinson (1965)Data of Galloway et al. (1970) Data of Verma (1974) Data of de Roo (1983) Data of Thakore and Holder (1987)Data of Yang et al. (2000)Calculated by Sloan (1998)Present calculation

Figure 2. Comparison of experimental and calculated equilibriumpressure of methane hydrate in three phase equilibria

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Three Phase Equilibria for Ethane Hydrates

Temperature / K

255 260 265 270 275 280 285 290 295

Pres

sure

/ M

Pa

0.1

1

10

Data of Robert et al. (1940)Data of Deaton Frost (1946)Data of Reamer et al. (1952)Data of Galloway et al. (1970)Data of Holder and Grigoriou (1980)Data of Ng and Robinson (1985)Data of Avlontis (1988)Calculated by Sloan (1998)Present calculation

Figure 3. Comparison of experimental and calculated equilibriumpressure of ethane hydrate in three phase equilibria

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Temperature / K

240 250 260 270 280 290

Pres

sure

/ M

Pa

0.1

1

10

Data of Wilcox et al. (1941)Data of Miller and Strong (1946)Data of Deaton and Frost (1946)Data of Reamer et al. (1952)Data of Robinson and Mehta (1971)Data of Verma (1974)Data of Thakore and Holder (1987)Data of Holder and Godbole (1982)Data of Patil (1987)Calculated by Sloan (1998)Present calculation

Figure 4. Comparison of experimental and calculated equilibriumpressure of propane hydrate in three phase equilibria

Three Phase Equilibria for Propane Hydrates

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Three Phase Equilibria for Mixed Hydrates

Figure 5. Comparison of calculated dissociation pressure of methane+ethane hydrate with measurements by Deaton and Frost (1946) for structure I

Temperature / K

260 270 280 290 300

Pres

sure

/ M

Pa

1

10

100

Methane in vapor = 100%Methane in vapor = 95.0%Methane in vapor = 90.4%Methane in vapor = 56.4%Methane in vapor = 0%Present calculation for pure methanePresent calculation for methane 95%Present calculation for methane 90%Present calculation for methane 80%Present calculation for methane 56%Present calculation for methane 30%Present calculation for methane 10%Present calculation for pure ethane

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Three Phase Equilibria for Mixed Hydrates

Temperature / K

270 275 280 285 290

Pres

sure

/ M

Pa

1

10

Ethane in vapor = 67.8%Ethane in vapor = 74.0%Ethane in vapor = 81.4%Ethane in vapor = 85.0% ~ 85.7%Ethane in vapor = 100%Present calculation for ethane 67.8%Present calculation for ethane 74.0%Present calculation for ethane 81.4%Present calculation for ethane 85.0%Present calculation for pure ethane

Figure 6. Comparison of calculated equilibrium pressure of ethane +propane hydrate with measurements for structure I hydrate

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Three Phase Equilibria for Mixed Hydrates

Temperature / K

270 272 274 276 278 280

Pres

sure

/ M

Pa

0.1

1

10

Ethane in vapor = 81.4%Ethane in vapor = 72.9~74.0%Ethane in vapor = 65.8~67.8%Ethane in vapor = 44.3~45.9%Ethane in vapor = 28%Ethane in vapor = 0%Present calculation for ethane 81.4%Present calculation for ethane 73.5%Present calculation for ethane 66.8%Present calculation for ethane 45.0%Present calculation for ethane 28.0%Present calculation for ethane 0%

Figure 7. Comparison of calculated equilibrium pressure of ethane+ propane hydrate with measurements for structure II hydrate

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Solubility of Methane in H-Lw Equilibria

Figure 8. Comparison of calculated methanesolubility in liquid water phase of H-Lwequilibria with present experimental data

Temperature / K

272 274 276 278 280 282 284

Mol

e fr

actio

n of

met

hane

in w

ater

0.0000

0.0005

0.0010

0.0015

0.0020

Present measurements at 5.1 MPaPresent measurements at 10.1 MPaPresent measurements at 12.7 MPaPresent measurements at 14.3 MPaRegressed value from Yang et al. (2001)Calculated value from Handa (1990)Regressed value of present experimentaldata at 273.15KLinear regression line of present experimental data

Temperature / K

272 274 276 278 280 282 2840.0005

0.0010

0.0015

0.0020

Present measurements at 5.1 MPaPresent measurements at 10.1 MPaPresent measurements at 12.7 MPaPresent measurements at 14.3 MPaPresent calculation

Figure 9. Comparison of present experimentalmethane solubility in liquid water phase of H-Lw equilibria with experimental data by Yang etal. (2001) and Handa's prediction (1990)

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Solubility of Ethane in H-Lw Equilibria

Temperature / K

274 276 278 280 282 284

Mol

e fr

actio

n of

eth

ane

in w

ater

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

Present calculation at 10.1 MPaPresent calculation at 15.1 MPaPresent calculation at 20.1 MPaPresent measurement at 10.1 MPaPresent measurement at 15.1 MPaPresent measurement at 20.1 MPa

Figure 10. Comparison of calculated ethane solubility in liquid waterphase of H-Lw equilibria with present experimental data

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Water Content of Hydrocarbon-Rich Phase in H-Πi Equilibria

Figure 11. Comparison of calculated water contents in methane-rich phaseof H-V equilibria with isobaric experimental data by Aoyagi et al. (1980)and Sloan's calculation (1998)

Temperature / K

230 240 250 260 270 280

Wat

er c

onte

nts /

ppm

0

50

100

150

200

250

Data of Aoyagi et al. (1980) at 3.45 MPaData of Aoyagi et al. (1980) at 6.90 MPaData of Aoyagi et al. (1980) at 10.34 MPaCalculated by Sloan (1998)Present calculation

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Water Content of Hydrocarbon-Rich Phase in H-Πi Equilibria

Figure 12. Comparison of calculated water contents in ethane-rich phase of H-ΠC2H6 equilibria with Sloan et al. (1986) andSong and Kobayashi (1994).

Temperature / K

250 260 270 280 290 300

Wat

er c

onte

nt /

ppm

10

100

1000

Data of Song and Kobayashi at 2.48 MPaData of Song and Kobayashi at 3.45 MPaData of Sloan et al. at 3.45MPaPresent calculation at 2.48 MPaPresent calculation at 3.45 MPaSloan's calculation at 2.48 MPa Sloan's calculation at 3.45 MPa

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Water content of hydrocarbon-rich phase in H-Πi equilibria for mixed hydrate

Figure 13. Comparison of calculated water contents in hydrocarbon-rich phase of H-L equilibria with isobaric experimental data of Songand Kobayashi (1994) for water+ethane+propane system at 3.45 MPa

Temperature / K

250 260 270 280 290 300

Wat

er c

onte

nt /

ppm

10

100

Ethane in liquid = 100%Ethane in liquid = 50%Ethane in liquid = 75%Ethane in liquid = 89.5%Calculated for ethane in liquid = 100%Calculated for ethane in liquid =50% Calculated for ethane in liquid = 75% Calculated for ethane in liquid = 89.5% Calculated for propane in liquid = 100%

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Water content of hydrocarbon-rich phase in H-Πi equilibria for mixed hydrate

Figure 14. Comparison of calculated water content in hydrocarbon-rich phase of H-Vequilibria with isobaric experimental data of Song and Kobayashi (1982) for water +methane + propane system, mole fraction of propane in vapor phase is 0.0531

Temperature / K

230 240 250 260 270 280 290

Wat

er c

onte

nt /

ppm

0

100

200

300

400

500

600

Data of Song and Kobayashi (1982) at 2.07 MPa Data of Song and Kobayashi (1982) at 3.45 MPaData of Song and Kobayashi (1982) at 6.89 MPaData of Song and Kobayashi (1982) at 10.34 MPaCalculated for 2.07 MPaCalculated for 3.45 MPaCalculated for 6.89 MPaCalculated for 10.34 MPa

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Conclusions

Solubilities in water-rich phase of H-LW for methane and ethanehydrate were obtained with the accuracy of 3.1 % and 5.3 % inmole fraction, respectively.

A unified calculation method was investigated with thenonrandom lattice fluid hydrogen bonding theory. The Kiharaparameters in vdWP model and the vapor pressure of the emptyhydrate were optimized.

With a single binary parameter and hydrogen bonding energy,various phase equilibria of simple hydrate and mixed hydratewere calculated with good accuracy.