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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%
Lattice Constant= 3.02 Å Eb= -0.889 eV Lattice Expansion= 1.34%
Lattice Constant= 3.01 Å Eb= -1.48 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
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?
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
Effect of surface func3onali3es
Perfect graphite slit-‐pore
Effect of surface func3onali3es
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
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?
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
Transport Downstream 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
Velocity x 10-5 (cm/sec)
-60
-40
-20
0
20
40
60
0 20 40 60 80 100
Velocity x 10-5 (cm/sec)
As pore sizes increase to 10 nm reduced wall interactions take place in the center of the pore
Upstream Pressure
Transport Downstream 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?