Click here to load reader

Constitutive Modeling of Chalk with Considering Effect of ... · PDF file Constitutive Modeling of Chalk with Considering Effect of Intergranular Physicochemical forces Changfu Wei(韦昌富)

  • View
    2

  • Download
    0

Embed Size (px)

Text of Constitutive Modeling of Chalk with Considering Effect of ... · PDF file Constitutive...

  • Constitutive Modeling of Chalk with Considering Effect of Intergranular Physicochemical forces

    Changfu Wei(韦昌富)

    Institute of Rock and Soil Mechanics

    Chinese Academy of Sciences

    Dec. 14-17, 2016, HKU

    IGSCSRM-2016, Hong Kong

  • 1971

    Oil production began

    Depletion method

    1984

    Oil field compression

    Settlement: 3 m

    1987

    Inject seawater

    Platform jacked up 6 m

    1993-1994

    Reservoir pressure recovered

    2007

    Total settlement: 8-9 m

    A notorious example: Subsidence of Ekofisk oil field

    Water-weakening effect of chalk

  • Microstructure and features of Chalk Material

    Coccoliths

    Rosettes Calcite

     “grains” originated

    from the skeleton

    of algae organism

     High porosity (40%

    - 50%)

     Large surface area

    (~2.0 m2/g)

     Chemically active

    SEM image 1 m

    Zeta potential data Equilibrium water: - 20 mV

    Methanol: +10 mV

    Oil: 0 mV

  • Our working hypothesis

     What is the relevance of these features

    Intergranular stress

    Hypothesis: Mechanical behavior of

    chalk is governed by Intergranular

    stress but NOT effective stress! op

    wpFree or capillary water ( )

    Adsorbed water ( ) w

    disjoiningp

  • Outline

    1. Surface forces & surface potential

    2. Matric potential & Chemical potential

    3. Pore water pressure & effective stresses

    4. Constitutive modeling of chalk

    5. Concluding remarks

  • 1. Surface forces and surface potential

    Surface forces in the soil pores saturated with water solution:

     capillary forces (in case of unsaturation)

     interactions between water dipoles and charged solid surfaces

     electrostatic forces (Columbic force)

     van der Waals forces

     hydrogen bonding forces

     diffuse double layer repulsion

     others …

  • 1. Surface forces and surface potential

     How to characterize these surface forces?

    ˆ f fA w A 

    f w 

    ˆf f fA A 

    【Definition】 Surface potential ˆ fA

    fA

    Porous medium Reservoir

    Solution (water) is moved

    slowly from the reservoir

    to the porous medium

    wWork input:

    Energy conserved:

  • Chemical potential of a species in the pore fluid

    , , ,

    ( )

    ( ) k

    k ff f m

    f f f f

    ff

    T Jn m k

    Jn A

    Jn  

     

     

     

    2. Matric and chemical potentials

    0 0( , , , , ) ( , ) ln ( , , ) ( , , ) j jk k k

    f ff f ff f f f f f k

    k k

    RT T p C n T p a T p C T n

           

    m m

    F

    Classical chemical potential

    Surface potential

    Definition:

  • Surface potential

    1. Between two bulk phase:

    2. In an individual phase:

    0 0( , , , , ) ( , , , , ) j jk k

    f gf gf f g gT p C n T p C n   

    0 0( , , , , ) ( ) jk

    ff f fT p C n const    g Z Z

    2. Matric and chemical potentials

     

    1

    0 +

    r

    f f f f

    r M D r

    S

    S s dS     Equilibrium conditions:

    H O H O2 2

    H O2

    2H O

    = ln

    f f

    W D f

    RT a

    a

           m

    Donnan osmotic pressure

    Matric suction

  • 3. Pore water pressure & effective stresses

    Equilibrium solution

    f f

    A Bp p k kf f

    A B  f f

    B Ap p 

    H O2 f f

    D    

    H O H O2 2

    H O2

    2H O

    = ln

    f f

    W D f

    RT a

    a

           m

     

    0

    1

    +

    r

    f f f f

    r

    M D r

    S

    S

    s dS

       

    

    What is the pore water pressure?

    Generalized osmotic pressure

  • 3. Pore water pressure & effective stresses

    H O H O2 2

    H O2

    2H O

    = ln

    l l

    W D l

    B

    RT a

    a

           m

    0

    l l

    D D      

    0 0.09 0.18 0.27 0.36 0.45 nl

    10

    100

    1000

    10000

    100000 

    D [

    k P

    a]

    c0 [moles/m 3]

    n = 0.45

    cfix= 100 [moles/m 3]

    1000 400

    100

    10

    rS

  • Effective stresses of unsaturated soils are given by

    Int

    op p   σ σ 1 1

    o w

    Ms p p Matric suction:

    Generalized osmotic pressure:

    Donnan osmotic pressure:

    Surface potential:

    = ln

    ww eq

    D w

    w pore

    aRT

    a

         

       m

    w w

    D     

     

    1

    0 =

    r

    w w w w

    r M D r

    S

    S S dS    

     Int r Mp S s 

    @ full saturation

    3. Pore water pressure & effective stresses

    wp   σ σ 1 1

  • Physical significance of average intergranular stress

    3. Pore water pressure & effective stresses

    w

    neutralp p 

    op

    wpFree or capillary water ( )

    Adsorbed water ( )

     For oil- AND water- saturated:

     For water-saturated

    w

    disjoiningp

    neutralp  σ σ 1

    op

    op

     

    (1 )

    1

    o w

    neutral r r

    r M r

    p S p S p

    S s S 

      

         

  • 3. Pore water pressure & effective stresses

    0 20 40 60 80 100 Sr [%]

    -100

    -80

    -60

    -40

    -20

    0

    p in

    tG R

    [ k P

    a ] c0 [moles/m

    3]

    n=0.6

    T=296 K

    cfix = 30 [moles/m 3]

    10

    100

    500

    0 20 40 60 80 100 Sr [%]

    1

    10

    100

    1000

    10000

    100000

      

    D o

    r s M

    [ k P

    a ]

    D

    sM

    n = 0.6

    T = 296 K

    c0 = 100 [moles/m 3]

    cfix= 30 [moles/m 3]

    The average intergranular stress ( ) in a clay during drying intGRP

    intGR

    1 P

    3 kk eqp  

  • 3. Pore water pressure & effective stresses

    -2 0 2 4 0

    2

    4

    6

    8

    10

    q (

    M P

    a)

    p' (MPa)

    Equilibrium water

    250g/l NaCl

    700g/l CaCl 2

    Glycol

    -2 0 2 4 0

    2

    4

    6

    8

    10

    q (

    M P

    a)

    p I ' (MPa)

    Equilibrium water

    250g/l NaCl

    700g/l CaCl 2

    Glycol

    Critical state line

    Failure lines for the chalks saturated by various fluids

    wp   1   w w wDp       σ σ 1 1Terzaghi: Current:

  • 3. Pore water pressure & effective stresses

    Apparent cohesive pressure of various chalks

    0 25 50 75 100 0

    1

    2

    3

    4

    c (M

    P a)

    Mole % water

    Traditional effective stress

    Intergranular stress

    High-porosity outcrop chalk (Risness et al. 2005)

    0.0 0.1 0.2 0.3

    1

    2

    3

    c (M

    P a)

    w

    Net stress

    Intergranular stress

    Lewes chalk (Taibi et al. 2009)

  • 4. Constitutive modeling of chalk

    M

    q

    p

    Oil-saturated

    Water-saturated c

    /c M  

    Constitutive framework: The Modified Cam Clay model

       0 0 Int,pc c vp p h p 

       0 0 0 0, exp exp p

    p v c v cp p

            

      

     

     Int Mrp S s 

       Int Intexph p p

    Intergranular PhysicoChemical pressure

    [email protected] 100% : 0, 1.0rS p h  

    0( 0 ) 

    0( 0 ) 

    cpcp

  • 4. Constitutive modeling of chalk

    Material parameters

    Conventional: (as in the Modified CamClay model)

    Physicochemical Effect:

    Water Retention Characteristics:

    *

    0, , , , , , cE M c p  

    0, ,fixc 

    , n

     

    1 1

    M

    1

    1

    n

    r n S

    s

        

     

Search related