Adsorption Models for Coalbed Methane Production and CO2 ... · Adsorption Models for Coalbed Methane Production and CO 2 Sequestration K. A. M. Gasem ... properties and coal matrix

November 12, 2004 1

Oklahoma State University

School of Chemical Engineering

Adsorption Models for Coalbed Methane Production and CO2 Sequestration

K. A. M. GasemR. L. Robinson, Jr.

(Principal Investigators)

Z. Pan J. E. Fitzgerald

M. Sudibandryio


Sponsored by theU.S. Department of Energy

November 12, 2004 2



Equilibrium Adsorption Modeling

§ We seek simple, reliable adsorption equilibrium models that are suitable for generalized predictions and reservoir simulations.

§ Such models should:

– Precisely represent pure and mixture isotherms

– Facilitate accurate a priori predictions based on gas properties and coal matrix characterization

Strategy: Use rigorous methodologies rooted in fundamentals to develop reliable methods of high industrial utility.

November 12, 2004 3



Excess Ads. = Vads (ρads- ρgas)

Pressure

Exc

ess

Ad

s.

§ At low pressures the isothermis nearly linear and ρads>>ρgas

Local Density Near Surface

Excess Adsorption: Near-Critical Behavior

November 12, 2004 4



Pressure

Exc

ess

Ads

.

§ At higher pressures the isotherm has some curvature




November 12, 2004 5



Pressure

Exc

ess

Ads

.

§ At higher pressures the isotherm has some curvature and an excess adsorption maximum is reached.




November 12, 2004 6



Pressure

Exc

ess

Ads

.

§ The isotherm shape will eventually change concavity.




November 12, 2004 7



Pressure

Exc

ess

Ads

.

§ The excess adsorption will pass through zero at sufficiently high pressures.



Excess Ads. = Vads (ρads- ρgas)Does this mean that coalbed reservoirs contain lessnatural gas at higher pressures?

November 12, 2004 8



Excess and Absolute Adsorptionand Gas Capacity

§ Even though the excess adsorption, nE passes through a maximum and eventually through zero,the absolute adsorption, nA increases with pressure.

Pressure

Ads

orpt

ion

Qua

ntity

§ The gas capacity, nGCdenotes how much gas (both adsorbed and unadsorbed) is in the volumetric container of arbitrary Vvoid.

nGC= nE+ ρgasρhelium1

φpack-1

nA= nE+ Vads ρgas

φpack =ρhelium

ρapparent=

Adsorbent volumeTotal volume

§ The excess adsorption is sometimes called the Gibbs excess adsorption because it assumes two distinct phases, the adsorbed phase, and the unadsorbed phase.

November 12, 2004 9



Comparison of Gibbs Excess, Absolute Adsorption and Gas-Capacity of Carbon Dioxide on Dry Activated

Carbon at 45°C

0

5

10

15

20

25

30

0 2 4 6 8 10 12 14

Pressure (MPa)

Adso

rptio

n o

r Am

ount

(mm

ol/g

)

Gibbs Excess, SLD ModelAbsolute AdsorptionGas-In-Place

0.529 g/cc Apparent Density

November 12, 2004 10



Experimental Facility

• Two experimental apparatuses are used in current studies.

• The mass balance approach is employed in both.

• Expected uncertainty in the measurements is estimated at:– 2% for the pure fluids – 6% for the mixtures




Vacuum Pump

Pressure Temp.

Heat Exchanger

Air Temperature BathRuska Pump

Vent

Water Heaterand Pump

Pressure

Equ

ilibr

ium

Cel

l

Mag

netic

Pum

p

Temp.

Vent

Air Temperature Bath

Motor

SamplingValve

Gas ChromotagraphHe CH4 CO2 N2 C2 He

Experimental DesignThe experimental method employs a mass balance principle, based on careful volumetric measurements.




§ Volumetric measurements§ Moisture content § PVT density predictions § Adsorbed phase density estimates

Factors Affecting Equilibrium CBM Adsorption Measurements




CO2 and Ethane Adsorption on Activated Carbon (OSU)

0

2

4

6

8

10

0 2 4 6 8 10 12 14

Pressure (MPa)

Adso

rptio

n (m

mol/g

)

Carbon Dioxide, Gibbs

Carbon Dioxide, Absolute

Ethane, Gibbs

Ethane, Absolute




0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 500 1000 1500 2000

Pressure, psia

Ads

orpt

ion,

mm

ol/g

Absolute Adsorption on Fruitland Coal at 115°F

CO2

Nitrogen

Methane




Mixture Adsorption on Illinois-6 Coal at 115°F

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 200 400 600 800 1000 1200 1400 1600 1800

Pressure (psia)

Abs

olut

e A

dsor

ptio

n (m

mol

/g c

oal) Pure CO2

Mixture Total

Pure CH4

CO2 in Mixture

CH4 in Mixture

LRC

Mixture is 60/40 CH4/CO2




0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0.0 0.1 0.2 0.3 0.4 0.5

Normalized Slit Width

Loca

l Den

sity

, g/c

cStrategy: Use rigorous methodologies rooted in fundamentals to develop reliable models…

Bulk Gas

Adsorbate

Mean Field Approximation




Molecular Interactions

Gas Molecule

z L - z

Coal Surface

( ) ( ) ( )zLzz 2fs1fsfs −µ+µ=µ

ff

fs1 fs2

ρwall = 1 / b

Local Density

Area / 2




Modeling Approach

§ Articulate the physics of the adsorption phenomenon.

§ Rely on VLE and PVT data to provide required model inputs for fluid-fluid (εff , σff ) interactions.

§ Generate fluid-solid (εfs, σfs ) interactions applicable to all models; e.g.,

– εfs is estimated from theory or regressed– L is obtained from matrix pore distribution or regressed– A is regressed or obtained from accessible characterization

§ For matrix characterization, seek the ability to utilize limited adsorption data involving only one fluid.




Selected Theories for Modeling High-Pressure Adsorption

§ Simplified Local Density Model(Rangarajan et al., 1995; Fitzgerald et al., 2003)

§ Ono-Kondo Lattice Model(Aranovich et al., 1996; Sudibandriyo, 2003)

§ Two-Dimensional Equation of State Model(DeGance, 1992; Zhou et al., 1994; Pan et al, 2003)




SLD-EOS AdsorptionModeling: An Example




The SLD model:

§ Provides a consistent theory which accounts for adsorbate-adsorbate (fluid-fluid) and adsorbate-adsorbent (fluid-solid) molecular interactions

§ Delineates the adsorbent structural properties based on assumed physical geometries of the adsorbent

§ Predicts the adsorbed-phase density, which facilitates prediction of absolute gas adsorption

Why the SLD Model?




The Simplified Local Density (SLD) Model

z L-z -

AdsorbentSurface

Adsorbed Phase

Bulk Phase[ ]bayPTf i

bulki ,,,,ˆ r

[ ]bzazxzPTf iads

i ),(),(),(,,ˆ rρ

[ ]zfsiΨ

( )( )

( ) ( )0

ˆ)(),(ˆ

ln =−Ψ+Ψ

+

kT

zLz

yf

zzxf fsi

fsi

bulki

adsi

r

r ρEquilibrium Relationship:




Fluid- Fluid Interactions within Slit

Fluid-Fluid Interactions

The fugacity near the surface is a function of position:

( )( )

−+

++

−

−

+

−−

−

−

=

∑∑

∑

21)(1

21)(1ln

)(

)()(2)(2

22

)(

)(ln1

)(

)(2

)(

)(ˆln

bz

bz

za

zazx

b

bbzx

RTb

za

RT

Pb

RTz

P

RTz

P

b

bbzx

Pzx

zf

jijj

jijj

jijj

i

adsi

ρ

ρ

ρρ

Bulk- Phase Interactions[ ][ ]bbRT

Ta

bRT

P

ρρ

ρ

ρρ )21(1)21(1

)(

1

1

++−+−

−=PR-EOS:




Fluid-Solid Interactions

ρwall = 1 / b

σff / 20.142 nmσ

ss = 0.335 nm

Slit Length L

Local Density

Area / 2

z

Depiction of a SlitWe use Lee’s partiallyintegrated (10-4) potentialmodel todescribe thefluid-solid interactions.

( ) ( ) ( )( )

( )( )[ ]

∑

σ−+′

σ−

′

σσεπρ=Ψ

=

4

1 4

4

10

102

12

1

54)(

iss

ifsifs

ifsifsatomsfs

iizz

z




Extending SLD to Mixtures

§ We set Cij and Dij to zero for all component interactions in the gas phase

§ We regress Cij (Dij=0) in the adsorbed phase

∑∑=i j

ijji axxa ∑∑=i j

ijji bxxb

( ) 2/)C1(aaa ijjiij −+= ( ) 2/)D1(bbb ijjiij ++=




Database Used§ We have assembled the OSU Adsorption Database

which contains pure, binary, and ternary mixture adsorption measurements conducted at Oklahoma State University on eight different matrices.

§ Included in the database are details regarding:- Adsorbates, adsorbent, temperature, pressure,

composition, and moisture content

- Gibbs and absolute adsorption in both SI and English engineering units

- The expected experimental uncertainty for each adsorption measurement




OSU Adsorption Database

0.7 – 13.7328.2CH4, CO2, N2, C2H6Dry Illinois #6, Beulah Zap, Wyodak, Upper Freeport, Pocahontas

Coal

77-81

0.7 – 13.7319.3CH4, CO2, N2Wet LB Fruitland Coal74-76

0.7 – 12.4328.2CH4, CO2, N2 MixturesWet Tiffany Coal70-73

0.7 – 13.7328.2CH4, CO2, N2Wet Tiffany Coal67-69

0.7 – 12.4319.3CH4, CO2, N2 MixturesWet Illinois #6 Coal64-66

0.7 – 12.4319.3CH4, CO2, N2Wet Illinois #6 Coal61-63

0.7 – 12.4319.3CH4, CO2, N2 MixturesWet Fruitland Coal58-60

0.7 – 12.4319.3CH4, CO2, N2Wet Fruitland Coal55-57

0.7 – 12.4318.2CH4, CO2, N2 MixturesDry AC – F 40051-54

0.7 – 13.7318.2CH4, CO2, N2, C2H6Dry AC – F 40047-50

Pressure Range (MPa)

Temp (K)

AdsorbateAdsorbentSys. No.




Literature Database

0.44 – 9.19178 - 298N2AC, Coconut shell 20

0.05 – 0.8 294 - 351CH4, CO2AC, Norit RB118-19

0.02 – 20.2303 - 318CO2AC, Calgon F-40017

0.09 – 9.40233 - 333CH4AC, Coconut shell 16

0.008 – 6.0 298CH4, CO2, N2AC, Norit R1 Extra 13-15

0.05 – 3.35278 - 328CO2AC, F30/470 12

0.11 – 6.69296 - 480CH4, CO2AC, PCB-Calgon Corp. 10-11

0.003 – 3.84213 - 301CH4, C2H4, C2H6, CO2AC, BPL 6-9

0.0 – 13.5283 - 333CH4, C3H8Charcoal4-5

0.026 – 1.50311 - 422N2, CH4, C2H6AC, Columbia Grade L 1-3


Temp (K)





Literature Database – 2

0.03 – 6.00 298CH4, CO2, N2 mixturesAC, Norit R1 Extra 43-46

0.12 – 2.97301CH4,C2H4,C2H6mixtures

AC, BPL39-42

0.14 – 15.02298CH4, C2H6Zeolite, 13 X 37-38

0.056 – 1.15283 - 303CH4, C2H4, C2H6Zeolite, G5 34-36

2x10-5 – 0.21283 - 368CO2, H2S, C3H8H-Modernite 31-33

0.03 – 17.61298 - 348CH4, CO2, N2, C2H6Zeolite, Linde 5A 27-30

0.35 – 8.23298 - 348N2Zeolite, Linde 13 X 26

0.03 – 14.56 298N2, CO2AC, Norit R1 24-25

0.05 – 9.5303 - 383N2, CH4, C3H8AC, F30/470 21-23


Temp (K)


CBM Adsorbates: CH4, CO2, N2, C2H4, C2H6, C3H8, H2S




Why Activated Carbon?

§ Modeling of adsorption behavior on coals is complicated by: - The difficulty in characterizing the coal matrix

adequately

- Assessing the effect of water on the adsorption behavior

§ Dry activated carbon provides a simpler reference matrix for modeling adsorption.

§ Desired models for adsorption on wet coals should apply readily for adsorption on dry activated carbon.




We have developed:

§ State-of-the-art SLD, OK and 2-D EOS models and mixing rules to represent CBM adsorption equilibrium of pure fluids and mixtures within their experimental uncertainties.

§ Generalized and matrix-calibrated models to provide accurate predictions within one to three times the experimental uncertainties.

§ Improved computational capabilities, including robust algorithms for solving adsorption equilibrium for a variety of models.

Model Development




§ Despite their different theoretical bases, in general, 2-D EOS, SLD, and OK models give comparable results in their correlative and predictive abilities based on the gas properties and the accessible characterization of the adsorbent.

§ Specifically the models:

1. Correlate pure component adsorption within the experimental uncertainties (4% AAD).

2. Predict all pure component adsorption within 10% AAD.

Model Development - 2




4. Correlate the total and individual component adsorption in the binary systems within the expected experimental uncertainties.

5. Predict total adsorption for the binary and ternary systems studied within the expected experimental uncertainties.

6. Predict the individual component adsorption in the binaryand ternary systems within twice the expected experimental uncertainties.

7. Matrix-calibrated models provide reasonable predictions for high-pressure adsorption, typically within twice the expected experimental uncertainties

Model Development - 3




Sample Results




SLD-PR Model Representation of Methane Adsorption on Various Wet Coals

0.0

0.2

0.4

0.6

0.8

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0Pressure (MPa)

Gib

bs

Ad

sorp

tio

n (

mm

ol/g

) .

Fruitland #2 at 319 KIllinois #6 at 319 KTiffany at 328 KLower Basin Fruitland at 319 K




SLD Component Nitrogen Adsorption inMethane/Nitrogen Mixtures on Dry AC

0

1

2

3

4

0 500 1000 1500 2000Pressure (psia)

Nitr

og

en E

xces

s A

dso

rptio

n (m

mo

l/g)

Methane/Nitrogen 80/20Methane/Nitrogen 60/40Methane/Nitrogen 40/60Methane/Nitrogen 20/80Pure NitrogenRepresentationPredictions




Summary of Pure-Gas Adsorption Using 2-D Peng-Robinson (PR) EOS

Regressing A and εfs for each system

Generalized predictions

0.60.0504.7432Coals

--0.6178.61922Activated Carbons

--0.1992.41922Activated Carbons

Regressing σm,0, δ and εfs for each system

0.60.0674.9432Coals

--0.1081.4 1922Activated Carbons

Regressing a, b, and k for each isotherm

WAAERMSE%AADNPTSAdsorbents




Deviation Plot of the Two-ParameterOK Model Results

-40.0

-30.0

-20.0

-10.0

0.0

10.0

20.0

30.0

40.0

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0

Pressure, MPa

% D

evia

tio

n

Overall AAD = 3.6 %




0.0

2.0

4.0

6.0

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0

Pressure, MPa

Gib

bs

Ad

sorp

tio

n, m

mo

l/g A

C

303 K323 K343 K362 K 383 K Two-Parameter OK ModelGeneralized OK Model

OK Model Predictions of Methane Adsorptions onDry Activated Carbon at Various Temperatures




CH4 Absolute Adsorption for CH4 / CO2 onWet Fruitland Coal

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Pressure (psia)

CH

4 A

bsol

ute

Ads

orpt

ion

(mm

ol/g

)

Pure CH4

80% CH4

60% CH4

40% CH4

20% CH4

Wong-Sandler - Case 2

One-fluid - Case 1




0.0

0.1

0.2

0.3

0.4

0.5

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0

Pressure (MPa)

Gib

bs A

dsor

ptio

n (m

mol

/g)

Pure CH4Total CH4 in Mixture

Pure N2N2 in MixtureTwo-BIP OK ModelOK Predictions

Gibbs Adsorption of a 50/50 Mole % CH4 / N2 Feed Mixture on Wet Tiffany Coal at 327.6 K




-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0

Pressure (MPa)

Gib

bs A

dsor

ptio

n (m

mol

/g)

TotalCO2CH4N2OK from PureOK form Pure & Binary

Total and Individual Gibbs Adsorption of a 10/40/50 Mole % CH4 / N2/CO2 Feed Mixture on Wet Tiffany Coal at 327.6 K




0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0

Pressure, MPa

Gib

bs

Ad

sorp

tio

n, m

mo

l/g A

C

CO2CH4N2C2H6OK ModelOK Predictions

Matrix-Calibrated OK Model Predictions of Pure-Gas Adsorption on Dry Activated Carbon at 318.2 K




0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0

Pressure (MPa)

Gib

bs

Ad

sorp

tio

n (

mm

ol/g

Co

al)

WyodakBeulah ZapIllinois-6PocahontasUpper FreeportTwo-Parameter OK ModelOK Predictions

Matrix-Calibrated OK Model Predictions of CO2 Adsorptions on Dry Coals at 328.2 K




Pressure (MPa)

0

5

10

15

20

25

0.0 2.0 4.0 6.0 8.0 10.0

CH

4A

bso

lute

Ad

sorp

tio

n (

mm

ol/g

)

Surface area and fluid-solid Interactionregressed based on 12 Data points 233 K

293 K

273 K

253 K

313 K

333 K

Matrix-Calibrated 2-D PR EOS Model Predictions of Methane Absolute Adsorption on Dry Activated Carbon




Closure§ The SLD-EOS, OK, and 2D EOS, frameworks are

effective for modeling high-pressure mixture adsorption.

§ The use of matrix-calibrated models will minimize the experimental effort required to obtain accurate adsorption predictions for a specific CBM site.

§ A potential exists for developing a priori predictive models using fully-generalized parameters determined by accessible adsorbate and adsorbent characterizations.




However! To fully exploit the potential of the models in CBM recovery and CO2 sequestration processes, we need to:

§ Develop a more rigorous approach to account for the effect of water on CBM adsorption systems.

§ Develop an accurate equation of state, which exhibits accurate hard-sphere limiting behavior, to improve modeling of high-pressure gas adsorption.

§ Systematically-selected measurements should be conducted to expand our database on mixtures adsorption and delineate the effects of moisture content and competitive adsorption.

Adsorption Models for Coalbed Methane Production and CO2 ... · Adsorption Models for Coalbed Methane Production and CO 2 Sequestration K. A. M. Gasem ... properties and coal matrix

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