Adsorption Modeling Update

11/15/2006 1

Oklahoma State UniversitySchool of Chemical Engineering

Adsorption Modeling UpdateK. A. M. Gasem

R. L. Robinson, Jr.(Principal Investigators)

J. E. FitzgeraldS. A. Mohammad

J. S. Chen

Oklahoma State University

Sponsored by theCoal-Seq II Consortium

November 2006

11/15/2006 2


Improved Adsorption Models for Coalbed Methane Production

and CO2 Sequestration

Our goal is to develop reliable coal-structure-based generalized equilibrium models that are suitable for

generalized coalbed methane (CBM) adsorption predictions and reservoir simulations.

11/15/2006 3


Measure pure CO2 adsorption isotherms on wetBeulah-Zap, Wyodak, Illinois #6, Upper Freeport, and Pocahontas #3 coals.

Measure the adsorption of pure methane, nitrogen, and CO2 on activated carbon at two levels of moisture.

Measure the adsorption of pure methane, and nitrogen on three wet Premium Argonne coals.

All measurements will be at 328.2 K and pressures to 13.8 MPa.

Experimental Program Modified Objectives

11/15/2006 4


Model Development Objectives1. Develop an equation of state (EOS) that is more

accurate at high densities (hard-sphere limit).

2. Develop robust algorithms to account rigorously for the presence of moisture.

3. Assemble a database for the adsorption of CBM gases on carbon matrices with special emphasis on coals.

4. Generalize the model parameters of the most successful of 2-D EOS, OK or SLD models in terms of accessible coal characterizations.

11/15/2006 5


First Year AccomplishmentsAcquired new adsorption data on five dry Argonne Premium coals. These data constitute a valuable addition to the CBM adsorption database.

Refined the Hard-Sphere EOS to include accurate predictions of water properties.

Demonstrated the ability of the SLD-HS framework to represent our data within their experimental uncertainties.

Developed SLD-HS model generalizations for dry coals.

11/15/2006 6


A Status ReportEffect of moisture on CO2 adsorption

CO2 adsorption on wet Pocahontas coal

CO2 adsorption on wet activated carbon at three levels of moisture

Water adsorption algorithm

Excess volume model for pure gas adsorption

EOS mixture adsorption modeling

Adsorption Database

Future work

11/15/2006 7


Experimental studies are underway to investigatehow moisture content may affect significantly the:

Adsorption capacityMixture adsorption behaviorData interpretation and reconciliationAdsorbed-phase density

Confirmation run completed for CO2 adsorption on wet Pocahontas Coal.

Measurements completed for CO2adsorption on wet activated carbon at 131 °F.

Moisture Effects

11/15/2006 8


Effect of Moisture Content on Gas Adsorption: Literature Observations

Presence of moisture reduces the gas adsorption capacity.

Moisture content above the equilibrium moisture level does not affect significantly the adsorption on wet coals.

The key question here is: Quantitatively, how does moisture level below equilibrium moisture content affect adsorption behavior?

Thus our focus is on isotherm adsorption measurements at more than one level of moisture.

11/15/2006 9


Effect of Moisture Content on Gas Adsorption: CO2 Adsorption on Pocahontas Coal at 131°F

0.0

0.4

0.8

1.2

1.6

2.0

0 400 800 1200 1600 2000 2400

Pressure (psia)

Exc

ess

Ads

orpt

ion

(mm

ol/g

)

Pocahontas Coal (Dry)

Pocahontas Coal (0.65% Moisture)

11/15/2006 10


Effect of Moisture Content on Gas Adsorption: Pure-Gas Adsorption on Wet Tiffany Coal at 130°F

0.0

100.0

200.0

300.0

400.0

500.0

600.0

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Pressure (psia)

Gib

bs A

dsor

ptio

n (S

CF/

ton)

N2 (11.7% Moisture)

CH4 (5.6% Moisture)

CH4 (16.5% Moisture)

CH4 (11.7% Moisture)

CO2 (11.7% Moisture)

11/15/2006 11


Determining Moisture Content of Activated CarbonAdsorption measurements were conducted on two levels of moisture (27% and 34% moisture).

A modified ASTM D1412 coal procedure was used to determine the moisture content of F-400 AC.

According to ASTM D1412 the equilibrium moisture for F-400 AC is about 27%.

Calgon Corporation claims that F-400 AC can hold up to 50% adsorbed water when soaked in water.

CO2 adsorption at 34% moisture content was lower than adsorption at 27% moisture.

Therefore, we suspect 27% moisture is below the saturation level of F-400 AC

11/15/2006 12


Effect of Moisture Content on Gas Adsorption: CO2 Adsorption on Activated Carbon at 131°F

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

0 200 400 600 800 1000 1200 1400 1600 1800 2000Pressure (psia)

Exc

ess

Ads

orpt

ion

(mm

ol/g

)

Dry

34% Moisture

27% Moisture

15 % Moisture

Changes in Concavity

11/15/2006 13


Effect of Density Correction: CO2 Adsorptionon Wet Activated Carbon at 131°F

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

0 200 400 600 800 1000 1200 1400 1600 1800 2000Pressure (psia)

Exc

ess

Ads

orpt

ion

(mm

ol/g

)

27% Moisture

27% Moisture (Density Correction)

5% Gas Density Correction

11/15/2006 14


Kinetics of CO2 Adsorption on Wet Activated Carbon

0

50

100

150

200

250

300

350

400

450

100 200 400 600 800 1000 1200 1400 1600 1800 2000Pressure Step (psia)

Equ

libra

tionT

ime

(hrs

)

27% Moisture

34% Moisture

11/15/2006 15


Kinetics of CO2 Adsorption on Wet Activated Carbon

Long equilibration times were observedEquilibration time for each pressure step lasted from one to three weeksLonger times were required for pressures below 1000 psia

Changes in concavity occurred below 1000 psia This may be attributed to (a) gas-phase CO2 stripping of moisture from the adsorbent, and/or (b) errors in the CO2 gas densities

11/15/2006 16


Effect of Moisture Content on Gas Adsorption: CO2 Adsorption on Illinois # 6 Coal at 131oF

0.0

0.4

0.8

1.2

1.6

2.0

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200Pressure (psia)

Gib

bs A

dsor

ptio

n (m

mol

/ g

Coa

l)

Dry coal

4% Moisture

8% Moisture

11/15/2006 17


Effect of Moisture Content on Gas Adsorption:Literature Data - 1

Joubert’s study on effect ofmoisture on CH4 adsorption on Pittsburgh I Coal at 30°C

Negligible effect of moistureabove the equilibrium level on CH4 adsorption

Gregory et al.,1986, found similar results for CH4

adsorption on a set of coalsfrom Black Warrior Basin

Dry

4% Moisture

11/15/2006 18


Effect of Moisture Content on Gas Adsorption:Literature Data - 2

Adsorption of CH4 on wet activated carbon at 25 C reported by Zhou et al., 2001

They found that complete drying of a wet activated carbon is not necessary

Moisture content of less than 2% actually enhances CH4adsorption over the adsorption for dry activated carbon

11/15/2006 19


Model Development

11/15/2006 20


Desired Attributes of a Generalized Predictive Adsorption Model

The ability to predict mixed-gas adsorption from pure-gas isotherms.

The ability to generalize the pure-gas isotherms from the characteristics of the coal.

Robust algorithms to account rigorously for thepresence of moisture in the coal.

Toward this end, we use our newly developed HS-EOS within the SLD adsorption theory.

11/15/2006 21


EOS Modeling ApproachExtend HS-SLD adsorption model to mixture predictions for dry and wet coals

Thus far we have generalizations for pure-gas adsorption on dry coals

Generalize PR-SLD model parameters for adsorption predictions involving pure gases and mixtures, including both dry and wet coals.

Thus far we have an adsorption model for pure gases and mixtures

11/15/2006 22


Modeling of Pure-Water AdsorptionModeling supercritical-gas adsorption allows forone possible adsorbed phase-density in a pore at a given pressure and temperature.

However, models of water adsorption (liquid or vapor)show multiple roots within the pore.

Gibbs Energy Minimization and Stability Analysisprocedures are used to determine the correct phaseof water in the pore.

11/15/2006 23


Adsorption of Water using HS-SLD Model

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 0.5 1 1.5 2 2.5 3 3.5 4Pressure (psia)

mas

s fra

ctio

n of

wat

er a

dsor

bed(

abso

lute

)

Dipole=1.00, L=1.2Dipole=0.80, L=1.2Dipole=0.60, L=1.2Dipole=1.00, L=5.0

11/15/2006 24


Accounting for the Moisture Effect: SLD-HS Model + Excess Volume Model

We use an excess volume term to represent themixture adsorbed-phase density in terms of the purecomponent adsorbed-phase densities:

( ) ( )Ex

20Hads

Abs20H

2COads

Abs2CO

adsvxx1 +

ρ+

ρ=

ρ

AbsO2H

Abs2CO

Ex xRTCxv =

The adsorbed-phase density, ρads, for CO2 is obtainedfrom the generalized SLD model. For water, the adsorbed-phase density is assumed to be 1.0 g/cc.

11/15/2006 25


Solution of Excess Volume Model

( )( )( )( )2CO,ads20H,ads

Ex2CO2COgas20H,ads

Ex20H,ads

Ex2CO2COgas20H,ads

Ex2COAbs

2CO /1y

v1yx

ρρ−ξ−ρ+ρ

ρ+ξ−ρ+ρξ=

For the CO2-water system, the absolute mole fractionof the adsorbed CO2 is obtained from a massbalance:

Ex,Totali

ExiEx

i nn≡ξwhere Abs,Total

i

AbsiAbs

in

nx =

( )igasAbsiadsads

Exi yxVn ρ−ρ=

11/15/2006 26


Solution of Excess Volume Model (Continued)

Given a trial solution of , the absolute mole fractioncan be explicitly written as:

Ex2COξ

( ) 4/1dxd2dd21x 2CO

idealAbs2CO2CO

22CO2CO

Abs2CO +−+±−=

( )( )RTCy2

11y1

d Ex2CO2COgas

2CO,ads20H,ads

Ex2CO2COgas

2COξ−ρ

⎟⎟⎠

⎞⎜⎜⎝

⎛

ρ−

ρξ−ρ+

=where

Adjust the trial solution until the following relationshipis satisfied: ( )

gasads

gasAbs

2COadsEx2CO

xρ−ρ

ρ−ρ=ξ

11/15/2006 27


Parameterization of Excess Volume Model

The excess volume constant C is a function of density:

AbsO2H

Abs2CO

Ex xRTCxv = gas29.0gas

1 CCC ρ+ρ

=

Constants C1 and C2 are functions of thefixed carbon (FC) content:

43

1 CFC100

CC +−

= 65

2 CFC100

CC +

−=

11/15/2006 28


Generalized Model of CO2 Adsorption on Beulah Zap Coal at 131 F

0.0

0.5

1.0

1.5

2.0

0 400 800 1200 1600 2000Pressure (psia)

Exce

ss A

dsor

ptio

n (m

mol

/g)

Beulah Zap (Dry)Beulah Zap (32% Moisture)

11/15/2006 29


Generalized Model of CO2 Adsorption on Pocahontas Coal at 131 F

0.0

0.4

0.8

1.2

0 400 800 1200 1600 2000Pressure (psia)

Exce

ss A

dsor

pion

(mm

ol/g

)

Pocahontas (Dry)Pocahontas (0.65% M oisture)

11/15/2006 30


Generalized Model of CO2 Adsorption on Upper Freeport Coal at 131 F

0.0

0.4

0.8

1.2

0 400 800 1200 1600 2000

Pressure (psia)

Exce

ss A

dsor

ptio

n (m

mol

/g)

Upper Freeport (Dry)Upper Freeport (1.1% Moisture)

11/15/2006 31


Generalized Model of CO2 Adsorption on Wyodak Coal at 131 F

0.0

0.5

1.0

1.5

2.0

0 400 800 1200 1600 2000Pressure (psia)

Exce

ss A

dsor

ptio

n (m

mol

/g)

Wyodak (Dry)Wyodak (28% Moisture)

11/15/2006 32


Generalized Model of CO2 Adsorption on Illinois Coal #6 at 131 F

0.0

0.4

0.8

1.2

1.6

2.0

0 400 800 1200 1600 2000Pressure (psia)

Exce

ss A

dsor

ptio

n (m

mol

/g)

Illinois #6 (Dry)Illinois #6 (9.2% Moisture)

11/15/2006 33


WAAE

Quality of HS-SLD Generalized Predictions for Adsorption on Coals

Overall WAAE is 0.81

i

N

i

calc nnabs

NWAAE ∑

=⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ −=

1 exp

exp1σ

Objective Function:

Methane Nitrogen CO2 Wet CO2

Beulah Zap 0.37 0.36 0.46 0.70Wyodak 0.34 1.07 1.32 0.36Ilinois #6 0.32 0.20 0.96 1.50

Upper Freeport 0.43 0.71 1.37 0.80Pochahontas 0.62 1.79 0.98 0.78

11/15/2006 34


Adsorption Database Assembly

11/15/2006 35


Adsorption Database An expanded adsorption database for CBM gases (CO2, CH4, N2) is being assembled.

Fifty-one new systems have been identified involving both pure

gases and mixtures.

Each “system” has at least one isotherm.

Database includes adsorption isotherms on coals and

activated carbon under wet and dry conditions.

Individual authors have been contacted to request their

numerical data.

11/15/2006 36


Future Work in Balance of Year 2Continue pure-gas adsorption measurements; specifically measure:

Methane and nitrogen on wet activated carbon

Methane and nitrogen on wet Argonne Premium coals

Evaluate mixing rules for the new HS-EOS.

Continue development of VLE / Adsorption algorithms.

Expand the model generalizations.

11/15/2006 37


2: Pure on Wet Activated Carbon

4: Model Generalization

3: Database Assembly

2: Algorithm Development

1: EOS Development

Model Development

3: Pure on Selected System

1: Pure on Wet Coals(Completed)

Experimental Work

Jan-May2007

Oct-Dec2006

Jul -Sep 2006

Apr -Jun 2006

Jan–Mar 2006

Oct-Dec 2005

Apr-Sep 2005

Task

Project Schedule

11/15/2006 38


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

11/15/2006 39


Molecular Interactions

Gas Molecule

z L - z

Coal Surface

( ) ( ) ( )zLzz 2fs1fsfs −µ+µ=µ

ff

fs1 fs2

ρwall = 1 / b

Local Density

Area / 2

11/15/2006 40


Molecular Interactions

Gas Molecule

z L - z

Coal Surface

( ) ( ) ( )zLzz 2fs1fsfs −µ+µ=µ

ff

fs1 fs2

ρwall = 1 / b

Local Density

Area / 2

11/15/2006 41


The Simplified Local Density (SLD) Model

z L-z -

AdsorbentSurface

Adsorbed Phase

Bulk Phase[ ]bayPTf i

bulki ,,,,ˆ r

[ ]bzazxzPTf iadsi ),(),(),(,,ˆ rρ

[ ]zfsiΨ

( )( )

( ) ( )0

ˆ)(),(ˆ

ln =−Ψ+Ψ

+⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

kTzLz

yf

zzxf fsi

fsi

bulki

adsi

r

r ρEquilibrium Relationship:

11/15/2006 42


Effect of Pressure on Excess Adsorption of Moist Systems

ωmix =ωCO2 + ωH2O

ω CO2 =ωCO2

At high p, ωH2O = 0 ???

At high p, ωmix =ωCO2

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