Carbon Capture Using Adsorption and Membrane Processes

Carbon Capture using Membrane and Adsorp3on Processes

Jennifer Wilcox Department of Energy Resources Engineering

RECS Summer School June 5th, 2012

Clean Energy Conversions Team -‐ 2012

•  Panithita Rochana (PhD) •  Yangyang Liu (PhD) •  Ekin Ozdogan (PhD) •  Jiajun He (PhD) •  Kyoungjin Lee (PhD) •  Abby Kirchofer (PhD) •  Ana Suarez Negreira (PhD, ChemE)

•  Tao Narakornpijit (MS) •  Jeremy Hoffman (UG, Chem) •  Reza Haghpanah (Post-‐doc) •  Dong-‐Hee Lim (Post-‐doc) •  Mahnaz Firouzi (Post-‐doc) •  Dawn Geatches (Post-‐doc) •  Erik Rupp (Research Assistant)

Agenda

Work and Cost of Carbon Capture N2-‐selecWve membrane for carbon capture Carbon-‐based sorbents for carbon capture

Minimum Work for Separa3on combined first and second laws

€

Wmin = RT nBCO2 ln(yB

CO2 ) + nBB −CO2 ln(yB

B −CO2 )[ ] + RT nCCO2 ln(yC

CO2 ) + nCC −CO2 ln(yC

C −CO2 )[ ]−RT nA

CO2 ln(yACO2 ) + nA

A −CO2 ln(yAA −CO2 )[ ]

Minimum Work for Separa3on

Published in APS Report, Feasibility of DAC with Chemicals (2011)

Sherwood Plot for Flue Gas Scrubbing

CalculaWons carried out using IECM, all cases assume 500-‐MW plant burning Appalachian bituminous, NGCC (477-‐MW) O&M + annualized capital costs are included in the cost esWmates

1Cost and Scale

Process Price [$/kg]

Concentra3on [mole frac3on]

Emissions [kg/day]

Cost [1000s $/day]

CO2-‐PCC 0.045 0.121 8.59 x 106 392

CO2-‐NGCC 0.059 0.0373 3.01 x 106 178

SOx (MS) 0.66 0.00127 8.94 x 104 59.6

SOx (LS) 2.1 0.000399 (399 ppm) 2.32 x 104 50.4

NOx 1.1 0.000387 (387 ppm) 1.11 x 104 12.5

Hg 22000 5 x 10-‐9 (ppb) 0.951 21.6

1These can change based upon coal-‐type burned and scrubbing methods; 2EN Lighdoot, MCM Cockrem, What Are Dilute SoluWons, Sep. Sci. Technol., 22(2), 165 (1987)

“the recovery of potentially valuable solutes from dilute solution is dominated by the costs of processing large masses of unwanted materials.”2 -Edwin Lightfoot

2nd-‐Law Efficiency Drops with Concentra3on

House, K.Z. et al., Proc. Nat. Acad. Sci., 108(51), 20428-‐20433 (2011)

η2nd =Wmin

Wreal

How to Increase the 2nd-‐Law Efficiency? Current State-‐of-‐the-‐Art Technology: Taking a closer look at ABsorpWon via MEA as an example:

1.  RegeneraWon 2.  Compression 3.  Blower/Fan 4.  Pumping

Regenera9on: Consider separaWon processes that do not involve solvents Compression: Consider separaWon processes that incorporate compression

Improvements:

Benefits of Adsorp3on and Membrane Processes

•  Both processes are based primarily upon physical separaWon processes, with CO2 maintaining its linear form throughout separaWon

•  Water does not need to be unnecessarily heated in either process; most solvents are aqueous-‐based w/ the chemical ~ 30 %

Membrane Process: •  Major challenge w/ CO2-‐selecWve polymers: lack of driving force in flue gas w/ CO2

concentraWon ~ 12 % -‐ consider N2-‐selecWve membrane instead •  Membranes have fairly small footprints and require no regeneraWon

Adsorp9on Process: •  Mesoporous carbons are scalable and can be cost-‐effecWve •  Carbons have opWmal heat properWes •  Major challenge w/ MOFs and zeolites: water compeWWon and acid gases –

consider chemistries in which H2O assists in the capture mechanism, recall flue gas water concentraWon is ~ 10 %

Agenda

Work and cost of carbon capture N2-‐Selec3ve Membrane for Carbon Capture Carbon-‐based sorbents for carbon capture

N2-‐Selec3ve Membrane for Carbon Capture

PhD students: Ni Rochana, Ekin Ozdogan, Kyoungjin Lee

•  Flux: Q = permeability, L = membrane thickness,

•  InspiraWon – ARPA-‐E brainstorm session in 2010 •  Capture CO2 on the high-‐pressure side of the membrane may lead to cost

savings in terms of compression energy •  System/OpWmizaWon will be crucial, but let’s see if it’s possible first

Feed

Residue (retentate)

Permeate

N2

Mem

bran

e

Step 1 Adsorp3on Step 2

Dissocia3on N2 N

N Step 3

Bulk Diffusion

N N N

H2 NH3

Poten3al Applica3ons: •  Carbon capture •  Ammonia synthesis •  Methane/N2 mixtures •  Air separaWon (selecWve O2) (IGCC, oxy-‐combusWon)

Goals: •  Use theoreWcal modeling to provide insight into tuning the electronic

structure of materials for enhanced nitrogen reacWvity •  Benchmark DFT predicWons with UHV experiments on single-‐crystal surfaces •  Perform permeaWon tests on the Group V materials

Mo3va3on for N2-‐Selec3ve Membrane

N2 Dissocia3on is Difficult!

•  Bond dissociaWon energies –  N2 ~ 225 kcal/mol; 944 kJ/mol; 9.7eV –  O2 ~ 119 kcal/mol; 498 kJ/mol; 5.1 eV –  H2 ~ 104 kcal/mol; 435 kJ/mol; 4.4eV

•  Common N2 dissociaWon catalysts (H-‐B, ammonia synthesis) –  Fe, Ru

•  d-‐band center model (Hammer and Nørskov) provides insight

The density of states (DOS) of a system describes the number of states at each energy level that are available to be occupied.

Density of States

unoccupied occupied

Fermi level

TransiWon metal reacWvity is disWnguished by its d-‐states, with each transiWon metal having a characterisWc d-‐band center

d-‐band Center Model

•  When bonding and anW-‐bonding states are formed, bond strength depends on the relaWve occupancy of states

•  Bonding states filled → strong bonds; anW-‐bonding states filled → weakening •  d-‐band center increases from R to L of periodic table (transiWon metals)

–  both bonding and anW-‐bonding states are higher from R to L –  Strength of adsorbate-‐metal bond increases

•  Why use Fe and Ru for ammonia synthesis? Why not Group V? –  answer → volcano

Hammer and Nørskov, Nature 376 238 (1995); Hammer and Nørskov, Adv. Catal. 45 71-‐129 (2000)

N and O Diffusivity in Vanadium Permeability = Diffusivity ×Solubility

1Keinonen et al. Appl. Phys. A 34, 39 (1984); 2Nakajima et al. Philosophical Magazine A 67, 557 (1993). 3Holleck, J. Phys. Chem. 74, 503 (1970); 4 Fukai and Sugimoto, Adv. In Phys. 34, 263 (1985)

Scope of Work

1. Surface ac3vity •  N2 adsorpWon mechanism •  N2 dissociaWon pathway •  Comparison to other typical

ammonia synthesis catalysts

2. Solubility and Diffusivity •  Atomic N binding

mechanism •  Comparison to atomic H

binding

3. Effect of alloying •  Ru •  Effect on binding •  ImplicaWons for

permeability

Computa3onal Methodology VASP (Vienna ab iniWo SimulaWon Package) Density funcWonal theory (DFT) •  Projector-‐augmented wave (PAW)

potenWal •  GGA – PBE

Bulk vanadium Lattice constant [Å]

This study 2.98

Previous calculation 2.93-2.941

3.0212

Experiment 3.0243

1Mehl and Papaconstantopoulos, Phys. Rev. B 54, 4519 (1996); 2Vitos et al., J., Surf. Sci. 411, 186 (1998); 3Online CRC Handbook of Chemistry and Physics, 91st ediWon, 2010-‐2011

Molecular N2 Adsorp3on Energy

1Grunze, et al., Appl. Phys. A 44, 19 (1987); 2 Bozso, et al. J. Catal. 49, 18 (1977); Ertl et al., Surf. Sci. 114, 515 (1982); 3Shevy et al., J. Phys. Chem. C 112, 17768 (2008)

strength of N2-metal bond increases

Eads (eV/molecule) = E(surf+N2) – [E(surf)+E(N2)] n(N2)

1 2 3

4

V(110)

1-top 2-short-bridge (SB) 3-long-bridge (LB) 4-three-fold (TF)

1 4

3

2

V(111)

1-top, 2-hcp 3-fcc, 4-bridge

Effect of Ru Addi3on

Ru Ru

+2.836

-0.09

-0.254 -0.257

-0.255

-0.141

-0.255

Pure Vanadium Distance (N-Ru)= 0.5 Å Distance (N-Ru)= 0.71 Å

+2.710

-0.292 -0.292

-0.292

-0.374 -0.292

+3.075

-0.235

-0.174

-0.372

-0.372

-0.214

+3.347 +3.075

Lattice Constant= 3.01 Å Eb= -2.132 eV Lattice Expansion= 1.01%



H binding in V: O-‐site = -‐0.076eV; T-‐site = -‐0.280eV

Aboud and Wilcox, J. Phys. Chem. C, 114(24) 10978-10985 (2010); Pauling-Scale Electronegativities: N = 3.04; V = 1.63; Ru = 2.2

Flux Measurements

Test Temperatures: 500°C -1000°C

Membrane Foils

(Group V metals) Diffusion Barrier

(uniformly rigidized sheet of alumina fiber and binder)

Porous Support

(Hastelloy X)

Inside of Membrane Holder

Sweep Gas

Permeate

Retentate

Feed Gas

Test Temperatures: 20 – 90 psi

•  Flux measurements:

•  Argon gas used to correct for pinhole and general leaks in the membrane system •  Each pure foil is tested at a temperature range of 500°C-‐1000°C. At each temperature,

feed pressure is changed between 23.4-‐93.4 psig. Retentate Pressure is kept at 3.4psig •  Use Knudsen diffusion for correcWons:

Membrane Defect Correc3ons

Gas Mixtures Niobium (ΔP=90 psi)

0.00E+00

5.00E-07

1.00E-06

1.50E-06

2.00E-06

2.50E-06

0.00E+00

5.00E-05

1.00E-04

1.50E-04

2.00E-04

2.50E-04

3.00E-04

0.001 0.0011 0.0012 0.0013 0.0014

CO

2 Flu

x ((

mol

e/m

·s)

N2 F

lux

(mol

e/m

·s)

1/T (K-1)

4 mol% CO2-96 mol% N2

N2 CO2

0.00E+00

1.00E-06

2.00E-06

3.00E-06

4.00E-06

5.00E-06

6.00E-06

7.00E-06

8.00E-06

0.00E+00

5.00E-05

1.00E-04

1.50E-04

2.00E-04

2.50E-04

0.001 0.0011 0.0012 0.0013 0.0014

CO

2 Flu

x ((

mol

e/m

·s)

N2 F

lux

(mol

e/m

·s)

1/T (K-1)

15 mol% CO2-85 mol % N2

N2 CO2

Natural gas flue gas Coal flue gas

Next Steps

•  ConWnue DFT calculaWons to predict alloys for enhanced N2 separaWon

•  InvesWgate subsurface and bulk diffusion predicWons of various alloys

•  Surface study experiments at SSRL to benchmark DFT

•  Repeat experiments with N2 flux in pure foils and invesWgate the potenWal of ammonia synthesis with H2 as a sweep gas

•  Work with SwRI to spuver deposit alloys of VRu and NbRu on porous stainless steel supports (Mov)

•  Measure N2 and CO2 fluxes of alloys and compare to pure

Agenda

Work and cost of carbon capture N2-‐selecWve membrane for carbon capture Carbon-‐Based Sorbents for Carbon Capture

Finding Ways Not to Bend CO2

Also cover design of “Carbon Capture,” Springer (2012) ISBN 978-‐1-‐4614-‐2214-‐3

How to Increase the 2nd-‐Law Efficiency? Taking a closer look at ABsorpWon as an example:

+

+

Envision a separa3on process that does not involve bending CO2

•  Slow kineWcs •  Highly exothermic

Closer Look at Heat Proper3es

Assume: Heat of regeneraWon = CpΔT + ΔH hea9ng up all material in system from T1 to T2 + breaking the CO2 interac9on

CCS Applica3ons of Carbon Materials •  SorpWon mechanisms in carbon-‐based sorbents and nanoporous

natural systems for sequestraWon are similar •  Cost-‐effecWve (carbon) and scalable (chemistry) sorbents •  Maximize sorbent capacity by surface chemistry •  Appreciate the importance of transport kineWcs, e.g., 500-‐MW

power plant emits ~ 11,000 tons of CO2 per day •  KineWcs: one of the main differences bet/ PCC and DAC

PhD Students: Yangyang Liu, Abby Kirchoffer, and Jiajun He

Research Associates: Mahnaz Firouzi and Erik Rupp

Molecular Simula3on

1.  Shale characterizaWon (XPS, SEM, Quantachrome, FTIR, etc.) for building accurate pore models

2.  Electronic structure theory -‐ decorate pore surfaces with accurate chemistry, i.e., clay, carbon, dissociated water, defect sites

3.  Grand Canonical Monte Carlo – predict adsorpWon isotherms and compare to experiment; –  How do fluid densiWes change at the nanoscale?

4.  Molecular Dynamics – predict transport properWes, e.g., permeability –  How does viscosity change at the nanoscale? Permeability?

Molecular Simula3on





Poten3al Models (L-‐J and TraPPE)

K00.28K 00.240

A40.3 A75.32

2

==

==

kk

CCO

CCO

εε

σσ

K9756.81

A571.32

2

=

=−

−

k

CCO

CCO

ε

σ

SchemaWc plot of one-‐center Lennard-‐Jones potenWal model of CO2 in slit-‐pore

Defining Adsorp3on •  Total Adsorp3on

Direct results from GCMC Modeling •  Excess Adsorp3on

Direct results from Lab Measurements •  Convert from Total to Excess AdsorpWon

Total Adsorbed – Bulk = Excess

Adsorp3on Isotherm Predic3on Based on PSD

Original PSD of AC sample

PSD truncated at 20 nm

Measured PSD → predict adsorp3on isotherm

•  Assume the total isotherm consists of a number of individual “single pore” isotherms mulWplied by their relaWve distribuWon over a range of pore sizes.

•  The set of isotherms for a given system can be obtained by GCMC simulaWons.

T = 305 K

•  Perfect graphite: the basic slit-‐pore surface •  Chemical heterogeneity: the possible funcWonal groups1 and the

mono vacancy site in the environment of volaWle components environment (e.g., water2) have been invesWgated

epoxy epoxy2 hydroxyl

carbonyl carbonyl - hydroxyl hydroxyl - carbonyl

H2O dissociate on the mono-vacancy

pore width

1Bagri, A. et al. J. Phys. Chem. C 2010; Kudin, K. N. et al. Nano LeW. 2008. 2Kostov, M.K. et al. Phys. Rev. LeW. 2005.

Effect of surface func3onali3es

Effect of surface func3onali3es Electronic properWes and parWal charge distribuWons by Density FuncWonal Theory (DFT)

parWal charge distribuWon

In general, oxygen-‐containing funcWonal groups increase the adsorbed CO2 density in micropores, especially in the cases of hydroxyl and carbonyl-‐funcWonalized slit pores;

0

5

10

15

20

25

30

0 50 100 150 200 250

Tota

l Loa

ding

[mm

ol/c

m3 ]

Pressure [bar] @ 298 K (pore width = 9.2 Å)

Perfect graphite Epoxy functionalized Hydroxyl functionalized Carbonyl functionalized Carbonyl_Hydroxyl functinoalized Hydroxyl_Carbonyl functionalized Carboxyl functionalized Hydrated graphite

0

5

10

15

20

25

30

0 50 100 150 200 250

Tota

l Loa

ding

[mm

ol/c

m3 ]

Pressure [bar] @ 298 K (pore width = 20 Å)

Perfect graphite Epoxy functionalized Hydroxyl functionalized Carbonyl functionalized Carbonyl_Hydroxyl functinoalized Hydroxyl_Carbonyl functionalized Carboxyl functionalized Hydrated graphite


Perfect graphite slit-‐pore


Perfect graphite slit pore

epoxy funcWonalized hydroxyl funcWonalized

carbonyl funcWonalized carbonyl_hydroxyl funcWonalized hydroxyl_carbonyl funcWonalized

hydrated graphite slit pore

carboxyl funcWonalized 1. Local density distribuWon is not homogeneous in the slit pores; 2. adsorbed layer has high density (> dry ice) → higher packing efficiency

Local CO2 density distribuWon

Effect of surface func3onali3es Compared to MOFs: •  At 1.0 bar, the loading

is up to ~12 mmol/g, compared to current state-‐of-‐the-‐art MOFs that range between 2~12 mmol/g at similar T and P

•  The pore size and

surface funcWonality of GCMC simulaWons is easily tunable to control adsorpWon

Supercritical CO2 @ 298K 250 bar Solid CO2 (dry ice)* Adsorbed CO2 in –COOH

@ 298K 1 bar

*CO2 Crystal structure data from AMCSD

Next Steps •  ConWnue GCMC to provide insight into opWmal funcWonality for enhanced

adsorpWon •  Surface funcWonalized (Zn-‐based) sorbents to catalyze the bending of CO2

– using controlled mesoporous carbons (collaboraWon w/ Bao and Stack) •  ConWnue PSD experiments and benchmarking w/ Quantachrome and

GCMC •  Carry out adsorpWon experiments with Rubotherm microbalance •  InvesWgate adsorpWon and breakthrough experiments using real flue gas

condiWons, i.e., water vapor, NOx, and SO2

triblock copolymers to template ordered mesoporous silica

Sorp3on and Transport at the Nanoscale Coal and Shale

•  Shale consists of organic (kerogen) and clay components with porosity on the nanoscale

•  Molecular simulaWon can determine the mechanisms of sorpWon and transport of fluids (CO2, methane, water) under nanoconfinement

•  Fluid properWes of interest may include: –  Density –  Viscosity –  Surface tension

•  We hypothesize that fluid properWes are different at the nanoscale vs macroscale due to: –  Pore size –  Pore chemistry (clay vs carbon vs surface funcWonality, e.g., dissociated

water) •  Improvements in understanding sorpWon and transport may influence

capacity esWmates and recovery, respecWvely

Research Outline

Coal / Gas Shale / Carbon-‐based Sorbents

Micro and Mesopores with Structural and

Chemical Heterogeneity

Slit Pores with FuncWonalized

GraphiWc Surfaces

AdsorpWon/Transport Measurements

Chemical ComposiWon, FuncWonal Groups,

PSD, etc.

Characteriza3on Quantachrome, FTIR,

XPS, SEM, etc.

•  AdsorpWon Isotherms •  Capacity EsWmates •  SorpWon Energy •  Permeability •  Transport Mechanism •  Slippage Factors

Modeling Electronic Structure,

GCMC, and MD

AdsorpWon Isotherms, PermeabiliWes

Carbon-‐ and Clay-‐based Materials

Compare

Sources and Sinks

Unmined coalbeds (ECBM)

Deep Saline Aquifers

Oil and Gas Reservoirs

Gas Shale Reservoirs (EGR)

CO2 sta9onary source in the U.S.

Overlap between sources and ECBM/EGR efforts

Making the Connec3on between Length Scales

Molecular Simula3on





Understanding Transport in Micropores Micropore < 2nm

•  Transport of equimolar binary mixture of CH4 and CO2 has been modeled using NEMD simulaWons in a slit pore model •  The pore wall is assumed smooth and the interacWon between molecules and pore wall was modeled by the Steele and fluid-‐fluid by the LJ potenWals •  Verlet algorithm was used to solve the equaWons of moWon

Upstream Pressure

Transport Downstream Pressure

Length = 15.2 nm [152 Å ] Width = micro to mesopore range

Upstream pressure = 3 atm, Downstream pressure = 1 atm, Temperature = 298 K

In small pores the velocity profile is plug flow and becoming parabolic at approximately 4 nm pores for CH4 and greater than 10 nm pores for CO2

CH4/CO2 Velocity Profiles in Micro and Mesopores

Upstream Pressure


-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

0 0.3 0.6 0.9 1.2 1.5

Z*

Velocity

-5

-3

-1

1

3

5

-0.3 0 0.3 0.6 0.9 1.2 1.5 Velocity

CH4

CO2

Height = 1.1 nm Height = 3.8 nm

-10

-6

-2

2

6

10

-0.3 0 0.3 0.6 0.9 1.2 1.5 Velocity

CH4

CO2

Height = 7.6 nm

Pure CH4, CO2 Velocity Profiles in Mesopores

Height = 10 nm

-60

-40

-20

0

20

40

60

0 20 40 60 80 100

Z (Å

)

Velocity x 10-5 (cm/sec)

-60

-40

-20

0

20

40

60

0 20 40 60 80 100


-60

-40

-20

0

20

40

60

0 20 40 60 80 100


As pore sizes increase to 10 nm reduced wall interactions take place in the center of the pore

Upstream Pressure


0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8 10 12 14 ΔP (atm)

CH4-76.2 CO2-76.2

0

2

4

6

8

10

0 2 4 6 8 10 12 14

Perm

eabi

lity

((gr

mol

e.cm

)/(m

in.c

m2 .a

tm))x

10- 3

ΔP (atm)

•  Gas permeability is enhanced for both components in micropores •  The permeability of CO2 is larger than CH4 due to the affinity of CO2 for carbon surfaces and lager density of CO2 in the pore and shielding effects

CH4, CO2 Permeability Versus ΔP

Height =11 Å Height =76 Å

M. Firouzi et al., Chemical Engineering Science 62, 2777 (2007)

50

•  The slippage factor and k∞ for CO2 is larger than CH4 as expected

•  As the pore becomes smaller the slippage factor and k∞ becomes larger due to the effect of the walls

CH4, CO2 Slippage Factor

Height =11 Å Height =76 Å

y = 0.0552x + 0.1922

y = 0.1969x + 0.2348

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.0 0.1 0.2 0.3 0.4 0.5 0.6 Inverse mean pressure (atm-1)

CH4-‐76.2

CO2-‐76.2

y = 1.7728x + 0.8412

y = 7.523x + 1.7447

0

2

4

6

8

10

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Perm

eabi

lity

((gr

mol

e.cm

)/(m

in.c

m2.

atm

))x10

- 3

Inverse mean pressure (atm-1)

CH4: K∞ = 0.84, b = 2.1 CO2: K∞ = 1.74, b = 4.3

CH4: K∞ = 0.19, b = 0.29 CO2: K∞ = 0.23, b = 0.84

kg= k∞(1+b/pm)

The viscosity near solid surfaces are spaWally varying and needs to be calculated using molecular dynamics:

Pure CH4, CO2 Slippage Factor

q/A=k/μ (-‐dp/dL)

Slit Pore: Height =11 Å

y = 19.104x + 3.8256 R² = 0.95475

y = 34.924x + 5.0398 R² = 0.98012

0

5

10

15

20

25

30

0.0 0.4 0.8 1.2 1.6 2.0

Perm

eability (m

d)

Inverse mean pressure (atm-‐1)

CH4 CO2

CH4: K∞ = 3.8, b = 5.0 CO2: K∞ = 5.0, b = 6.9

Pore network: Average pore size = 2 nm, Porosity = 20%

y = 3950.5x + 84.295 R² = 0.83745

y = 4840.6x + 85.585 R² = 0.98903

0

100

200

300

400

500

0.02 0.03 0.04 0.05 0.06 0.07

Perm

eability (nd)

Inverse mean pressure (atm-‐1)

CH4 CO2

CH4: K∞ = 84, b = 47 CO2: K∞ = 85, b = 56

kg= k∞(1+b/pm)

•  The viscosity increases with increasing

nanotube size and its value is lower than that under bulk condiWon

•  The noWon of viscosity, as used in classical conWnuum mechanics, may not be truly applicable

•  The computed values should be considered as apparent viscosity, as computed by the Einstein’s and Green-‐Kubo relaWons

M. Khademi, S. Sahimi, The Journal of Chemical Physics 135, 204509 (2011)

Water Viscosity in Nanotubes

Dependence of water viscosity modeled using MD on the diameter

of CNTs and SiC nanotubes

204509-3 Pressure-driven water flow in SiC nanotubes J. Chem. Phys. 135, 204509 (2011)

computed by two methods. One was the atom-based methodfor the summation of the all the contributions. The secondmethod that we used was the Ewald summation techniquein order to check the accuracy of the first method. The re-sults with the two methods were in agreement with eachother within their estimated errors. The rest of the termsthat contribute to E take on the standard forms that mostforce fields use. For example, the contribution by the bond-stretching term is given by, Es =

!4i=2[ki(! ! !0)i], and by

the angle-changing term by, E" =!4

i=2[ei(" ! "0)i], whereki is a stretching constant, ! and !0 the length and equilibriumlength of a bond, ei an angle-changing constant, and " and "0

are the angle and equilibrium angle between a pair of bondsthat are joined together at an atom. The numerical values ofall the constants are given by COMPASS.

Single-wall SiC nanotubes of type 1, the zigzag (m, 0)type, were utilized in the MD simulations with m = 6, 9, 12,and 16 and initial diameters of 0.59, 0.89, 1.19, and 1.59 nm,respectively. The length of the nanotubes was 5.3 nm. Thewater molecules were represented by the three-site SPC/Emodel.54 The van der Waals radius of water is still largerthan the SiC ring size. The Nosé-Hoover thermostat was usedto hold the temperature at 298 K. The Parrinello-Rahmanmethod,55 a feature of the commercial simulator with COM-PASS, was used for keeping constant the external pressuresat both ends of the nanotubes. The method was used becauseit allows both the simulation cell’s shape and volume to bemodified. To ensure that the pressures were held constant cor-rectly, we also used the standard Andersen method56 for keep-ing the pressures constant at the nanotubes’ ends. The resultswith the two methods did not differ significantly.

Temperature was held at 298 K. The time step for in-tegrating the equation of motion was 1 fs. Simulations of atleast 50 ps long were needed to establish the flow of water un-der a pressure gradient and to reach steady state, after whichthe first 50 000 time steps were ignored and then the numeri-cal data were collected over a minimum time of 25 ps. Equalnumbers of Si and C atoms were, of course, used.

Water viscosity in the nanotubes was estimated from theEinstein relation,

µ = kBT

3#dDz

, (9)

where T is the temperature, kB the Boltzmann’s constant, d thediameter of water, and Dz its axial diffusivity that is estimatedusing the Green-Kubo relation:

Dz = 1N

N"

i=1

# "

0#vi(t) · vi(0)$dt , (10)

where vi(t) is the axial velocity of molecule i at time t, and Nis the total number of molecules. The bracketed quantity rep-resents the velocity autocorrelation function (ACF). In smallnanotubes the diffusivity Dz is dependent upon the tubes’ di-ameter. We did not assume that the atomistic structure of thenanotubes is rigid, so that the C and Si atoms could movein response to their environment in the presence of the watermolecules and the applied pressure gradient according to theequation of motion.

FIG. 2. Axial velocity autocorrelation function in the smallest and largestSiC nanotubes that were studied.

IV. RESULTS AND DISCUSSION

Figure 2 presents the axial velocity ACF in the smallestand largest nanotubes that we simulated. It declines sharplyafter a short time, and then varies very little around zero. Aspointed out by Rahman and Stillinger,57 for liquids a diffusivemotion is present that destroys rapidly any oscillatory motion.Thus, the velocity ACF may exhibit one much damped oscil-lation (one major minimum) before decaying rapidly to zero,a description that is consistent with Fig. 2. Moreover, it hasbeen illustrated that damping in MD calculation does not af-fect the dynamic properties of a system to within the statisticaluncertainty.58 Fast dissipating behavior, similar to what we re-port, has also been commonly observed and used to calculatethe properties of water in the CNTs.

Figure 3 presents the computed viscosity µ of water andits dependence on the nanotubes’ diameter. For comparison,

FIG. 3. Dependence of water viscosity on the diameter of SiC nanotubes.For comparison the viscosity of water in CNTs (Ref. 47) is also given.

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•  The dimensions of the system modeled are ~ 10 x 10 x 10 nm •  3-‐D molecular pore network model based on the Voronoi tessellaWon method •  To generate the molecular pore network model:

-‐ Create a 3-‐D simulaWon box of structural atoms corresponding to porous structure -‐ Tessellate the atomic structural box

•  The pore space is created by specifying the desired porosity and # polyhedra → total volume fracWon = specified porosity

-‐ pore space consists of interconnected pores of various shapes and sizes

3-‐D Pore Network Model

Modeling Transport with MD

•  The pore network model previously described will be used •  Non-‐equilibrium molecular dynamics (NEMD) simulaWons are carried out

•  The system (pore network) is exposed to an external driving force (chemical potenWal or pressure gradient) in a specified direcWon

•  Flux and permeability predicWons are carried out

Permeability of N2/CO2 and CH4/CO2 Mixtures

Permeability of N2 / CO2 (lec) and CH4 / CO2 (right) mixtures with average pore diameter of 1.2 nm and 20%, 25%, 30% and 35% porosi9es

0

1

2

3

4

5

6

7

8

10 15 20 25 30 35 40

Permeability

((grmole.cm)/(min.cm2 .atm))x10

-7

Porosity

0.88 N20.12 CO20.75 N20.25 CO20.5 N20.5 CO20.25 N20.75 CO2

0

1

2

3

4

5

6

7

8

9

10 15 20 25 30 35 40 Porosity

0.75 CH4

0.25 CO2

0.50 CH4

0.50 CO2

0.25 CH4

0.75 CO2

•  With mixtures of N2, at high CO2 concentraWons, permeability is lower below a 30% porosity •  With mixtures of N2, 25% CO2 has the greatest permeability •  In gas mixtures of N2 and CH4, CO2 is always the more permeable species in 1.2 nm pores

Acknowledgements

•  CollaboraWons with Mark Zoback and Tony Kovsceck (shale research) •  CollaboraWons with Dan Stack and Zhenan Bao (sorbent research) Funding: •  Membrane: NSF Eager, Catalysis Division; EPA P3 (high-‐T furnace); Army

Research Office •  Sorp3on: BP; DOE-‐NETL; GCEP •  GCMC; MD: Stanford Center for ComputaWonal Earth & Environmental

Science •  DFT: NSF Teragrid, UT AusWn

Ques3ons?

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