basic field cycling relaxation features of liquids in ...the physics of liquids in porous media 1 0...

J.-P. Korb, School of FC NMR relaxometry, Mede, 1-3 June 2009 1

Basic field cycling relaxation features ofliquids in porous media

J.-P. Korb

[email protected]: 33 1 69 33 47 39

Collaborations: P. Levitz, D. Petit, R.G. Bryant


Academical Interest of studyingthe physics of liquids in porous media

1000Å

• Dynamics of liquids at solid interfaces

• Transport in porous media (filtration, imbibition, conduction)

• Role of surface physical chemistry(interaction and wettability)

• Phase transitions in confinement

• Hydration of proteins, DNA et biological tissues

• MRI (origin of contrast)

Vycor (P. Levitz)


Industrial applications

• Microstructure of cements (Durability)

• Nuclear waste materials

• Oil recovery

• Environnement: filtration of water

• Transport of fluids in soils

• Gaz separation

• Chemical reactivity (catalyst)

• Food stuffs

CSH

CH = Portlandite

Capillary pores


Field cyclingrelaxometry

Position of FFC relaxation in multiscale NMR

Length

Time

1Å 1nm 10 nm 0.1µm 1µm 10 µm 100 µm 1 mm 1 cm

Pulsed field gradient

10 ps

1 ns

1 µs

1 ms

100 ms

1 s MRIImaging

Bulk dynamicsTortuosity

Texture

Conventionalrelaxometry

T2,T1 T1(ω0)

Physical chemistrySurface dynamicsExchange, interaction, wettability

Spectroscopy

3D Transport

B0

( ) 00 /6 ωω DD =l

ω0 = γB0(Spin clock)

ω0τc=1


Outline

• 1. Intramolecular dipolar relaxation by translational diffusion at solid interfaces

• 2. Intermolecular dipolar relaxation by translational diffusion at solid interfaces

Dipolar relaxation processes in porous media


How is it possible to measure the surface relaxation from the overall 1/T1(ω0)? Model of biphasic fast exchange

(Fe3+ ?)

(Fe3+?)

Averaging between slowly relaxing “bulk” molecules and rapidly relaxing “surface” molecules (one T1 and 2 phases): τex << T1

S

V

ε( ) ( )0,1,101

111ω

εω surfacebulk TV

STT

+=

T1,bulk

T1,surface


Bulk liquids

1/T1 ∝ -τmln(ωτm)

2.211,1,1

≈≈Oil

Water

WaterOil DD

TT

Fast and local molecular motions, nofrequency dependence

Surface diffusion enhances the probabilityof 1H – Fe3+ reencounters

Physical-chemistry onsurface

Τ1 ∝ D ∝ 1/η

1/T1,bulk=Cte


Nuclear magnetic dispersion of liquids in pores

2.211,1,1

≈≈Oil

Water

WaterOil DD

TT

Fast and local molecularmotions, no frequencydependence

Surface translationaldiffusion enhances theprobability of 1H – Fe3+

reencounters

Fe3+

Physical-chemistry onsurface: aprotic vs proticliquidsBonding to paramagneticimpurities

Fe3+

1/T1=1/T1,bulk+(ε S/V)1/T1,surf(ω0)

1/T1,bulk=Cte

J.-P. Korb,S. Godefroy, MRI 21, 193 (2003)

Reservoircarbonate rock


Aprotic liquids in calibrated microporous glasses beads with paramagnetic impurities


S. Stapf, R. Kimmich, J. Chem. Phys. 103, 2247 (1995)Bioran and vycor d=4nmNo paramagnetic impurities

Evidence of a liquid dynamicsat surface, in presence ofa frozen bulk

R. Kimmich and E. Anoardo,Progr. in Nucl. Magn. Reson Spectr. 44, 257 (2004)

Polar liquidStrongadsoprtion

Non polar liquidWeakadsorption

Reorientation mediatedby translational dynamics (RTMD)


I. Intramolecular dipolar relaxation by translational diffusion of liquids atsurfaces of porous media

R. Kimmich and E. Anoardo, Progr. in Nucl. Magn. Reson Spectr. 44, 257 (2004)P.E. Levitz, J.-P. Korb, D. Petit, Europhys.J. E 12, 29 (2003)P.E. Levitz, J. Phys. Cond. Matter 17, S4059 (2005)P.E. Levitz, J.-P. Korb, Europhys. Lett. 70, 684 (2005)

Outline


In science, in fact in most things, it isusually best to begin at the beginning

Lewis Carroll


Modeling the intramolecular relaxation at surface

timeadsorption average=Aτ

Reorientation mediated by translational diffusion (RTMD) R. KimmichIntermittent Brownian Dynamics near a flat surface P. Levitz, J.-P. KorbPeriods of relocation in bulk L alternate with adsorption A on the surface

p.d.f. at long times for a flat surface

I(t)B0 L

AA

LH2O

I(t+τ)

( )τLΨ

( ) ( ) activatedEyringA

AA ,/exp

τττ

τ−

=Ψ

ωd

Relaxation due to magnetic noiseInduced by molecular dynamicsat proximity (or on) the flat surface

HD,intra(t)


P.d.f. ΨL(t) at long times for a flat surface given by the bridge statistics over a plane : a Brownian 1D dynamics

DDD BBB 123 ⊗=

( ) ( )( )

( ) ( )

( )

( ) ( ) ( ) )(12

1 Constraint ,2/

/2

22

,2

'' diffusion, Fo

,'')',(

timeslongat finds one paths,Brownian 1Ddifferent theallover Summing

/),(

/,0/

2/3LL3

2

L

2/122

L

2

22

pdfParetot

tdttDtDR

Rt

DtRDRt

DRt

dRttRJt

RdRrdCRJ

RrrCrrCC

Lτδδ

δδ

δδδ

=Ψ⇒=Ψ⇒=≈Ψ

=⇒==

−≈Ψ

==

−=

==∂∂=∆

∫

∫

rδ

R

0

1

r/R

δ

First returnat time t

t=0 x

τL= Minimum loop duration


ωd

Random modulation of Intramolecular interaction( ) ( ) ( ) ( ) ( ){ }( ) ( ) ( )[ ]

( ) ( ) ( ) ( ) ( ) ( ) ( )

( )

( ) ( ) ( )( ) ( ) ( ) ( )∑

∑

∫

−−−=−−=

≡−

−−==

+=−−=−=

+∝

=+=

+

∞+

∞−

jiji

jid

ii

i

ttttItItL

tLtItI

ttHitLtI

tItIdttItItItIG

JJRGFTJtItIG

,

2''2

2

0001

0

)()1('*'

*

functions Heaviside of Sum)()()(

)(*

,24,,

δω

τττ

ωωω

τωττ


Summing all the events i->j assuming no correlationbetween successive temporal events

( ) ( ) ( ) ( )∑ −−−=−−= +

jiji

jid ttttItItL

,

2'''2 )()1('* δω

)(tLΨ)(tAΨ

( )tδ2−

-ΨΑ(t) ∗ΨL(t) -ΨL(t)* ΨA(t)+ΨL(t) *ΨA(t) *ΨL(t) + ΨA(t)*ΨL(t)*ΨA(t)+…


( )

( )

( ){ } ( ){ } { } { }

..)(~)(~)(TF)(TF)(*)(F

~F

ansformFourier tr theofProperty

/ω0tLfor which events thealso adding

)(*)(*)()(*)(*)()(*)(2)()()(2/0

''2

''2

2d

''2

2''2

ωω

ω

δω

LALALA

ALA

LALLALAd

ttttT

LtLT

ttttttttttttL

ΨΨ=ΨΨ=ΨΨ

=

≤

ΨΨΨ+ΨΨΨ+ΨΨ−Ψ+Ψ+−=≥

( ) ( )( ) ( )( )( ) ( )( ) ⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

ΨΨ−

Ψ−Ψ−−∝

ωωωω

ωωLA

ALdL ~~1

~1~1Re2

serieslgeometrica theSumming

2''2


( ) ( ) ( )

( ) ( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )[ ]ASurfaceASurfaceASurface

A

LA

AAA

AAdASurface

AAAA

AA

LLL

L

JJR

LJ

i

iPareto

ωωωωωω

τπτ

ω

ωω

ωω

ωω

ωτωωωω

ωττωωτ

τττ

ωτπωτ

ττ

,4,,

surfaceflat afor 2

,

21

/,

1~,/exp

...1221~),(1

2

0,1

22/3

2

2

22

2/12/12/3

+∝

=

⎟⎟⎠

⎞⎜⎜⎝

⎛++

∝∝

−−=Ψ−

=Ψ

++−=Ψ=Ψ

( ) ( ) ( )( ) ( )( )( ) ( )( ) ⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

ΨΨ−

Ψ−Ψ−∝−=

ωωωω

ω

ωω

ωω

LA

ALdLL ~~1

~1~1Re

212

2''222

Not a single power law


Theoretical dispersion R1 (ω0)varying the average adsorption time

2

2

2 Awater

waterA D τ

δω =

( ) 2/10 /

1

Aωω

( ) ( ) ( )[ ]2/300

2/10 /5.0//

1

AAA ωωωωωω ++

0.01 0.1 1 10

1.5

2

3

5

7

10

15

20

Frequency (MHz)

R1

(s-1

) ωA = 0.12 MHz, τA = 5.5 ns

ωA = 835 MHz, τA = 64 ps

R1,bulk

Drastic changes of R1(ω0) with ωA

τA


1H

2H Intramolecularrelaxation

Reorientation translational mediated diffusion of water on themulticonnected interfaces of vycor (d=7nm)

(no paramagnetic impurities) P. Levitz, J.-P. Korb, D. Petit, Eur. Phys. J. 12, 29 (2003)

3D off-lattice reconstruction of thepore network from SAXS, MET

1000Å

Dsurface= Dbulk/4

Loop

OH

H

τL =10 ps

τA=5 ns EA = 10 kT

τesc= 3.5 µs

R1 ∝ 1/f1/2

ωA=0.1 MHz

Model of orientation memory of the director n(t)


Application of proton field cyclingrelaxometry to plaster pastes

• H. Jaffel, J.-P. Korb, J. Ph. Ndobo-Epoy,V. Morin, J.-P. Guicquero,J. Phys. Chem. B 110, 7385 (2006)

• H. Jaffel, J.-P. Korb, J. Ph. Ndobo-Epoy, J.-P. Guicquero, V. Morin, J. Phys. Chem. B 110, 118401 (2006)

• J.-P. Korb, P.E. Levitz, Magnetic Resonance in Porous Media: AIP Conf. Proc. Vol 1081, 55 (2008)


Objectives1. Probe the average adsorption time of water at the surface

of plaster paste by proton-water field cycling relaxometry

2. Vary the physical-chemistry at surface of plaster and relate this measurement to nanowettability

=> Improve the mechanical properties of this building material


Plaster paste

10 µm

βCaSO4,½H2O(solid)

10 µm

CaSO4,2H2O(solid)

Disordered polycrystalline (needle shape) porous material

Fragile microstructure Possibility of alteration, dehydration of gypsumcrystal, Shrinkage of porous network, …

Necessity of a non destructive technique of characterization

w/p=0.8

CaSO4, ½H2O(solid) + 3/2 H2O(aq) CaSO4, 2H2O(solid)

Hemihydrate Gypsum

Hydration

DissolutionPrecipitation

No paramagneticimpurities


Dissolution / precipitation

NMR degree of hydration and setting

CaSO4, ½H2O(solid) + 3/2 H2O(aq) CaSO4, 2H2O(solid)

Transverse magnetization

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅⎟⎟

⎠

⎞⎜⎜⎝

⎛−= φα

exp)()(

/)0,0(

),0(1)(

pwpw

MtM

t stoihydrhydr

H. Jaffel, J.P. Korb, J. Phys. Chem. B, 110(37) 18401 (2006).

NMR Degree of hydration

Setting


( ) 2/10 /

1

Aωω

( ) ( ) ( )[ ]2/300

2/10 /5.0//

1

AAA ωωωωωω ++

0.01 0.1 1 10

1.52

3

5710

1520

Frequency (MHz)

R1

(s-1

)

Biphasic fast exchange model verified by the rescaling data( ) ( )0,1,101 ωεω Surfacebulk RVSRR +=

Proton field cycling relaxometryallows separation of bulk and surface relaxation processes

( ) ( )0

0,1

0

01

ωω

φερ

ωω

ddRS

ddR SurfacepGyp

⎟⎟⎠

⎞⎜⎜⎝

⎛=

Same surface relaxation processwhen varying W/P

1H R1(ω0) data at various W/P after setting

1

10

10-2 10-1 100 101

0.50.4

0.60.8

R1 (s

-1)

Frequency (MHz)

W/P

CA +− 85.00ω

φ(%

)

70

60

50

40

301.00.80.60.4

w/p10-2

10-1

100

101

102

103

10-2 10-1 100 101

der 0.5der 0.6der 0.8

y = 0.70492 * x^(-1.8755) R= 0.97362

y = 0.601 * x^(-1.7936) R= 0.99777

y = 0.48932 * x^(-1.8758) R= 0.98541

-(dR

1/df) no

rmal

ized

Frequency (MHz)

CtegmS p ≈≈ ερ,/1 2

J.-P. Korb, P.E. Levitz, Magnetic Resonance in Porous Media: AIP Conf. Proc. Vol 1081, 55 (2008)

R1bulk


Proton and deuterium R1(ω0)

Same power laws for R1(ω0) of 1H and 2H

Intramolecular relaxation processby reorientational water dynamics at surface

10-2

10-1

100

101

102

103

104

10-2 10-1 100 101

0.5 H2O

0.6 H2O

0.8 H2O

0.5 D2O resc

Frequency (MHz)

(dR

1/df) no

rm

ω0

−1.85


1

10

10-2 10-1 100 101

1%6.5%

0.6%

R1 (s

-1)

Frequency (MHz)

0.12

0.18

875.2

ωΑ(MHz)

STMP/P (%)

Modifying the surface chemistry of plaster by adjuvant

W/P=0.6STMP

R1 decreases

5.5 ns

4.5 ns

64 ps

τA

due to reduction of τA and decrease of number of accessible sites on 010 surface

( ) ( )( ) 2/1,101 // −+= AVSbulk NNARR ωωωEvolution to

When increasing the amount of STMP

W/P = 0.8

W/P = 0.8 + 1% STMPAnisotropic growing

Isotropic growing


Conclusion on plaster pastes• The frequency dependence of the longitudinal relaxation rate of

proton-water in plaster pastes depends drastically on the physicalchemistry on the gypsum surface

• This allows us to probe directly the average adsorption time of water

• We succeed to change the physical chemistry of the surface of gypsum needles by adding adjuvant in the wetting water. It results a net decrease of the average adsorption time of water at the surface of gypsum polycrystals.

• These measurements are relevant to probe directly the wettability of plaster pastes at the nanoscale. This is useful to control the mechanical properties of this important building material


II. Intermolecular dipolar relaxation by translational diffusion of liquids at surfaces of porous media

• J.-P. Korb, M. Whaley, R.G. Bryant, Phys. Rev.E 56, 1934 (1997)• J.-P. Korb, M. Whaley, Th. Gobron, R.G. Bryant, Phys. Rev.E 60,

3097 (1999)• S. Godefroy, J.-P. Korb, M. Fleury, R.G. Bryant, Phys. Rev.E64,

021605 (2001)• S. Godefroy, M. Fleury, F. Deflandre,J.-P. Korb, J. Phys. Chem. B

106, 11183 (2002)

Outline


Translational diffusion of liquids in micropores

• Systems: calibrated poroussilica glasses (R=38Å and 80Å) with paramagnetic impuritiesFe3+ (40 ppm) fully saturated by aprotic liquids and water

• Objective : Probe the surface diffusion coefficient Dsurf

• Experiment: Proton magneticrelaxation dispersion data 1/T(ω0)

R

Fe Fe

Acetone

( ) ( )SSurfbulk TVS

TT ωωε

ω ,111

0,1,101+≈

Dsurf

Model of biphasic fast exchangeτex << T1


1/T1/T11((ωω00) of ) of aproticaprotic liquidsliquids in confinementin confinement

J.-P. Korb and R.G. Bryant, PRE 56, 1934 (1997)

0.01 0.1 1 10. 100.0123456

0.01 0.1 1 10. 100.0123456

1/T 1

(s-1

)1/

T 1(s

-1)

Frequency (MHz) Frequency (MHz)

Frequency (MHz)

Acetone 5°C

Acetone 75Å

75Å 75Å

159Å 159Å

Acetonitrile 5°C

0.01 0.1 1 10. 100.0123456

Frequency (MHz)

5°C

45°C

Acetonitrile 75Å

0.01 0.1 1 10. 100.0123456

5°C

45°C

0.01 0.1 1 10. 100.0123456

1/T 1

(s-1

)

Acetone 159Å

5°C

45°C

Frequency (MHz)0.01 0.1 1 10. 100.0123456

Acetonitrile 159Å

45°C

5°C

bulk

Fe3+

Dsurf << DVol

2D diffusionof proton bearing

moleculesat proximity of

Fe3+

1H species


1T1I

=23

γ Iγ Sh( )2S(S +1)

13JL

(0) ω I − ωS( )+ JL(1) ω I( )+ 2JL

(2 ) ωI + ωS( )⎡ ⎣

⎤ ⎦

JL(m )(ω) = GL

(m ) (τ )− ∞

∞

∫ eiωτdτ,

GL(m )(τ) = FL

(−m )( t)FL(−m )* (t + τ )

FL(−m) (t) = FM

( −m') (t)m' =−2

+2

∑ D−m,m'(2)* (α = 0, β, γ = 0),

= FPAS( −m") (t)

m"=−2

+2

∑ δm",0Dm' ,m"( 2)* (ϕ, θ, 0)

⎛

⎝ ⎜ ⎞

⎠ ⎟

m'= −2

+2

∑ D−m,m'( 2)* (α = 0, β, γ = 0),

It is much simpler to makethe calculations in the lamellar frame Mand use the well-known properties of theWigner matrices to go to the lab frame L

=6π5

1r 3( t)

Y2(m') θ(t ), ϕ( t)( )

m' =−2

2

∑ d−m,m'(2 ) (β ).

FPAS (0)(t)=√(3/2)/r3, FPAS

(±1)(t) = FPAS(±2) (t) = 0.


FL(−m )(t) = f 2

(m' ) (t)eim'ϕd−m,m'(2)

m '= −2

+2

∑ (β ),

f 2(0)( t) =

12

32

2z2 − ρ2

z 2 + ρ2( )5/ 2 , f 2(±1)( t) = m

32

ρzz2 +ρ 2( )5/ 2 , f2

(±2) (t) =34

ρ2

z 2 + ρ2( )5/ 2 .

GL(m) (τ ) = d−m,m'

(2 ) (β )d−m ,m"(2 ) (β ) f 2

(m' ) ρ0 ,z0( )f2(m") ρ,z( )ei m' ϕ0 −m"ϕ[ ]

m' ' =−2

+2

∑m' =−2

+2

∑

GL(m )(τ) = d−m,m'

(2) (β )d−m,m"(2) (β ) dϕ00

2π

∫ d2ρ0 dz0(CMz )∫

(CMρ )∫ p(0) f 2

(m' ) ρ0, z0( )ei m' ϕ0[ ]

m' '= −2

+2

∑m' = −2

+2

∑

dϕ0

2π

∫ d2ρ dz(CMz )∫

(CM ρ )∫ P ρ,ϕ, z,τ ρ0 ,ϕ0 ,z0, τ = 0( )f 2

( m") ρ, z( )e−i m "ϕ[ ].

Here α, β, γ are the Eulerian angles that rotate the L basis into the M basis. Because of cylindrical symmetry around n, we have chosen these angles asα = γ = 0; thus Dmm‘

(2) (α=0, β, γ=0) = dmm‘(2) (β) (Wigner rotation coefficients)

Ensemble average over a diffusing propagator

(in cylindrical coordinates)


P(r ρ ,z, τ

r ρ 0 ,z0 ,τ = 0) = P⊥ (

r ρ , τ

r ρ 0 ,τ = 0)P/ / (z,τ z0 ,τ = 0)

P⊥ (τ = 0) = δ (r ρ −

r ρ 0 ), P/ / (τ = 0) = δ (z − z0 ),

∂∂zP/ / (z = 0, τ) =

∂∂zP/ / (z = d,τ ) = 0.

P⊥r ρ ,τ

r ρ 0,τ = 0( )=

12π

dk k exp(−k2DI⊥τ0

∞

∫m=−∞

+∞

∑ ) Jm (kρ)Jm (kρ0) exp[im(ϕ0 − ϕ)],

P/ / z, τ z0,τ = 0( )=1d

1+ 2 exp −l2DI / / τd2

⎛

⎝ ⎜ ⎞

⎠ ⎟ cos

lπzd

⎛ ⎝

⎞ ⎠ cos

lπz0

d⎛ ⎝

⎞ ⎠

l=1

∞

∑⎡

⎣ ⎢ ⎤

⎦ ⎥ .

P ρ,ϕ,z,τ ρ0 ,ϕ0, z0 ,τ = 0( )≈1

2πddk k exp(−k2DI⊥τ

0

∞

∫m=− ∞

+ ∞

∑ )Jm(kρ)Jm(kρ0 )exp[im(ϕ0 − ϕ )].

GL(m) (τ ) = d−m,m'

(2) (β )2GM

(m') (τ),m' =−2

+2

∑

Anisotropyof diffusion

At long times (low frequency) P// tends rapidly to 1/d and GL//(m)(t) Cte

DDD BBB 123 ⊗=


At long times (low frequency)

JM(0 ) (ω) =

3πσsτ⊥

2d2δ' 2 lndδ'

+1⎛ ⎝

⎞ ⎠ − 3.078 +

14

ln 1 +1

ω 2τ⊥2

⎛

⎝ ⎜ ⎞

⎠ ⎟ +O ωτ⊥( )⎡

⎣ ⎢ ⎤

⎦ ⎥ ,

JL(0)(ω ) = d0,m'

(2) (β )2JM

(m' )(ω )m'= −2

+2

∑ =15JM

(0)(ω ) + 2 JM(1)(ω ) + 2 JM

(2)(ω)[ ]≈15JM

(0) (ω),

JL(1)(ω ) = d1,m'

(2) (β )2JM

(m' )(ω )m '= −2

+2

∑ ≈15JM

(0)(ω ),

JL(2)(ω ) = d2,m'

(2) (β )2JM

(m' )(ω )m'= −2

+2

∑ ≈15JM

(0) (ω).

Powder averages

GM(0) (τ ) ≈

38

πσS

d2δ' 2τ⊥

τ⎛ ⎝

⎞ ⎠ , GM

(1)(τ) ≈14

πσS

δ ' 4τ⊥

τ⎛ ⎝

⎞ ⎠

2

, GM(2)(τ) ≈

116

πσS

δ '4τ⊥

τ⎛ ⎝

⎞ ⎠

2

.

At long times (low frequency)


NMRD for different pore sizes and diffusion coefficients

0.01 0.1 1 10. 100.02468

101214

0.01 0.1 1 10. 100.02468

101214

1/T 1

(s-1

)1/

T 1(s

-1)

Frequency (MHz)

Frequency (MHz)

0.25

0.55 (a)

(b)

Pore size effect

50

75

159

Diffusion effect DI⊥ (10-6cm2/s)

d (Å)d(Å)

1T1I

=π

15σS γ I γ Sh( )2

S(S +1)τ⊥

d 2δ' 2 10 lndδ '

+1⎡ ⎣

⎤ ⎦

−30.8 +14

7ln 1 +ω S−2τ⊥

−2( )+3ln 1 + ω I

−2τ⊥−2( )

⎡

⎣ ⎢

⎤

⎦ ⎥

⎧ ⎨ ⎩

⎫ ⎬ ⎭ ,


Experimental NMRD for aprotic solvents

Dsurf << DVol


Experimental NMRD for aprotic solvents


Anomalous Temperature effects (surface vs volume)

∂P rIS ,τ( )∂τ

= Deff T( )∆ SP rIS ,τ( )1

10

3 3.2 3.4 3.6

1/T 1 (s

-1)

1000/T

0.01

0.04

0.1

0.250.41.0

4.010.030.0

ν (MHz) 75Å

(a)Em=4.8 kcal/mol

∆E < 0

Deff T( ) = n0 exp Es

RT⎛ ⎝

⎞ ⎠ D0 exp −Em

RT⎛ ⎝

⎞ ⎠

= Deff0 expEs − Em

RT⎛ ⎝

⎞ ⎠ with Es > Em

∆E = Em-Es = -2.6 kcal/molAnomalous temperature effect

Bulk

Fe

OH H

O OO

Si

O

Si

OO

O

OH

OH

OH

H

Pore surface

τm

OH

H

O

H

H

OH

H

τex

EmDiffusion

EsSurface

interaction

Water


Granular packings

SiC 25% Silice dgrain={8,…,150 µm}

10-1 100 101 102 1030

Dis

tribu

tion

(u.a

.)

T2 (ms)

Empilement de grains de 8 µmsaturé à l'eau

Dis

trib

utio

n

φ = 53%

0.01

0.1

1

10

100

101 102

K (D

arcy

)

dgrain

(µm)

K (D

arcy

)K ∝ (dgrains)2

Ions Fe3+

0 2000 4000 6000

Sign

al (u

.a.)

Champ magnétique (gauss)

g=2g~4.5

10 c

mFe3+ e-

S. Godefroy, J.-P. Korb, M. Fleury, R.G. Bryant,

Phys. Rev.E64, 021605 (2001)


Universal results for water in granular packings of SiC andmicroporous silica glasses

0.60.70.80.91.0

2.0

3.0

3.1 3.2 3.3 3.4 3.5

1/T 1(s

-1)

1000/T (K)

0.10.6312

6.310201625

0.016

(MHz)Huile

2

3

4

56789

10

3.1 3.2 3.3 3.4 3.5

1000/T (K)

0.010.10.41.62

6.3

2516

(MHz)

1/T 1(s

-1)

Eau

Granularpacking8µm

∆E >0

∆E >0

∆E<0

Water

Oil

1

10

3 3.2 3.4 3.6

1/T 1 (s

-1)

1000/T

0.01

0.04

0.1

0.250.41.0

4.010.030.0

ν (MHz) 75Å

(a)

Microporoussilica glasses


φ=24%, K=1,7mD, intermediate wettability

0

2

4

6

8

10

12

0.01 0.1 1 10

1/T 1 (s

-1)

Fréquence (MHz)

Eau

Huile

65°C

65°C

Application of FFC to reservoir carbonate rock

0

2

4

6

8

10

12

0.01 0.1 1 10

1/T 1 (s

-1)

Fréquence (MHz)

Eau

Huile

65°C

65°C

45°C

45°C

0

2

4

6

8

10

12

0.01 0.1 1 10

1/T 1 (s

-1)

Fréquence (MHz)

Eau

Huile

65°C

65°C

25°C

25°C

0

2

4

6

8

10

12

0.01 0.1 1 10

1/T 1 (s

-1)

Fréquence (MHz)

Eau

Huile

65°C

65°C12°C

10°C

0

2

4

6

8

10

12

0.01 0.1 1 10

1/T 1 (s

-1)

Fréquence (MHz)

Eau

Huile

65°C

65°C12°C

10°Cτm = 1,2 ns

D ≈ 10-7 cm2/s

Water: bilogarithmic NMRDDiffusion 2D with surface interaction

Oil: quasi- bilogarithmic NMRDDiffusion 2D with surface interaction

1

2

3

4

5

6

7

0.01 0.1 1 10

Huile carbonate de carrièreHuile carbonate de réservoir

Fréquence (MHz)1/

T 1 (s-1

)


Conclusion

Calibrated andnatural porous media

Theories and simulationsMolecular dynamics at surfaces

FFC experimentsIn various conditions

of temperature, liquids,surfaces

ApplicationsHydration of proteins

Oil recoveryHydration and setting of cements and concretes

basic field cycling relaxation features of liquids in ...the physics of liquids in porous media 1 0...

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