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Application of Centrifuge Testing in Geo-Environmental Engineering

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Application of Centrifuge Testing in Geo-Environmental Engineering Powered By Docstoc
					Environmental Geomechanics
  and Transport Processes

           Patricia J. Culligan
   Department of Civil & Environmental
           Engineering, M.I.T

          INEEL Workshop, 2003
         Outline of Presentation
• Centrifuge Testing
   – Uses of Geocentrifuge
• Scaling Relationships
• Limitations
• Example Study
• Conclusions




                         INEEL Workshop, 2003
           Centrifuge Testing
Two basic uses of geocentrifuge:
1. Simulation of a “prototype” event
2. Investigation of “system” behavior




                    INEEL Workshop, 2003
Principle of Centrifuge Testing
Use centrifugal acceleration to simulate
  gravitational acceleration
                                                                w

                                                    r

    g

                                                 rw2 = ng

    Prototype - full-scale                   Model - scale1/n

                      INEEL Workshop, 2003
                     Result
         (r g z)prototype = (r ng z/n) model

r = density
z = macroscopic length

Similitude in stress/ pressure obtained between the
  scale model and the prototype


                    INEEL Workshop, 2003
             1. Traditional Use
Physical modeling of a specific problem (the
  „prototype‟)



     100 m

                       1m


                                            Strain
 Prototype      Model at 100 g           Data Point
                  INEEL Workshop, 2003
  Centrifuge has Unique Advantages
1. The magnitude and gradient of soil and/or fluid pressure
   are important to the problem

E.g., Soil (or geologic structure) is dependent upon level of
   stress




                        INEEL Workshop, 2003
Fluid Behavior Dependent Upon Pressure




              INEEL Workshop, 2003
2. Body (gravitational) forces are important to the
  problem


  E.g., Fluids of contrasting density interacting, or vadose
  zone behavior




                        INEEL Workshop, 2003
Subsurface DNAPL Transport
        Vapor plum e       Release

                                           Vadose zone


     Sand aquifer
                                       G roundw ater

                                              flow

     D issolved
     plum es                               D N A PL pool




                         Pools in
                         fractures            Residual
                                              blobs
            Bedrock aquitard


                    INEEL Workshop, 2003
          Uses of Geocentrifuge
Perform scale modeling of subsurface contaminant transport
  and remediation events in a controlled laboratory
  environment
   – Assess general technology performance
   – Investigate site-specific behavior
   – Data for theoretical model validation




                       INEEL Workshop, 2003
                     Mathematical Models
                        [full, simplified]
                                                      Direct modeling
                                                        of prototype
Learn mechanism of
transport processes
Verification/ Improvement of
theory


              Scale Physical Model                          Prototype

                [centrifuge model]                         [actual field
                                                             problem]

                               INEEL Workshop, 2003
              2. Alternative Use
Investigation of system behavior over range of
  conditions


    1m             1m               1m


  10 g          50 g           100 g
                                                  Strain

   Same Model; different g-levels              System Behavior

                        INEEL Workshop, 2003
          Uses of Geocentrifuge
Investigate the influence of body (gravitational forces) on
  subsurface transport
   – Gain fundamental understanding
   – Construct “phase diagrams” that can be used as design
     tools


      No other experimental technique is as versatile as the
                 centrifuge in this respect

                         INEEL Workshop, 2003
              Scaling Relationships
Scaling relationships are important if centrifuge test data need
  to be translated to prototype data

Usual Given Relationships (n = scaling factor)

Parameter                    Protoype/ Model Ratio
Gravity, g                           1/n
Macroscopic Length, L (Z)            n
Microscopic Length, d (r)            1        (prototype material used)

  ALL OTHER RELATIONSHIPS NEED TO BE DERIVED FOR SPECIFIC
        EXPERIMENTAL CONDITIONS, AND THEN VALIDATED

                               INEEL Workshop, 2003
            Often Assumed Relationships

Parameter                     Protoype/ Model Ratio

Intrinsic Permeability, k                 1          n = Scaling Factor
Fluid Viscosity, Density,
    Interfacial Tension u, r, s           1          (prototype fluids used)
Medium Porosity, n                        1
Fluid Pressure, P                         1
Pore Fluid Velocity, v                    1/n
Hydraulic Conductivity, K                 1/n
Time, t                                   n2         (transport “accelerated”)



                                  INEEL Workshop, 2003
  Deriving Scaling Relationships
Partial inspectional analysis
Dimensional analysis

Both require some knowledge of processes important
  to the problem




                     INEEL Workshop, 2003
Validating Scaling Relationships
Use technique of “modeling of models” - scaled
  centrifuge test data is compared to prototype data

       Very Important to ALL Model Testing




                    INEEL Workshop, 2003
           Interesting Pressures
Pressure        Prototype/ Model Ratio



Hydrostatic     rgz                 1
Seepage         vmz/r2              1
Capillary       2scosq/r            1
Body            Drgz                1



                 INEEL Workshop, 2003
         Dimensionless Numbers
Number                    Prototype/ Model Ratio


Re          (vrd/m)                  1/n   d = micro
Pe          (vd/Dd)                  1/n   L = macro

Ca(micro)   (vm/s)                   1/n
Bo(micro)   (rgd2/s)                 1/n
Ca(macro)   (vmL/ds)                 1
Bo(macro)   (rgdL/s)                 1

                  INEEL Workshop, 2003
         What is Not Possible
Acceleration of “real-time-processes”
E.g., radioactive decay, microbial decay, NAPL
  dissolution, etc.


Duplication of complexity found in field



                   INEEL Workshop, 2003
               Other Issues
Increased fluid velocities
  – Scaling problems with processes that are
    velocity dependent (e.g, miscible dispersion)


Capillary Entrapment
  – Scaling problems with micro-scale entrapment



                   INEEL Workshop, 2003
Centrifuge has proven very advantageous in
 investigating physical mechanisms of fluid
 and contaminant transport in controlled
 systems




                 INEEL Workshop, 2003
Example Study




   INEEL Workshop, 2003
DNAPL Behavior in Fractures
    Vapor plum e      R elease

                                      Vad ose zo ne      Excavation, SVE
                                                            Porous media
S and aquifer
                                    G rou ndw ater
                                                           Pump and treat,
                                          flow
                                                           enhanced P&T,
 D issolved                                                  air sparging
 plum es                              D N A P L p ool
                                                        Plume control: feasible
                                                        Aquifer cleanup: difficult

                                                               Fractured
                    P oo ls in
                    fractures             R esidual             media
                                          b lobs
        B edrock aquitard                               No known formula for
                                                        successful remediation
                             INEEL Workshop, 2003
       Geocentrifuge Modeling
Used to investigate physics of DNAPL behavior in a
  smooth-walled vertical fracture

   – Objective to provide insight into processes controlling
     problem in simple system




                       INEEL Workshop, 2003
        Physics of the Problem
    Field Scenario                  Experimental Modeling

          DNAPL pool
H
                                      H

                                                     Reservoir tube
                Fracture
L               initially
                saturated with         L             Simulated
                water (under                         fracture
                hydrostatic
                conditions)
                                              r
          e            INEEL Workshop, 2003
  Condition Before DNAPL infiltrates the
                 fracture
                                              Water
  Water                                                DNAPL

DNAPL Pool                         H
                                            Pressure
                 DNAPL-                                 Static
                 water                                  pressure
                 interface                              difference

 The static pressure difference at the DNAPL-water interface
   is equal to Dr g H where Dr is the density contrast
   between water and DNAPL
                     INEEL Workshop, 2003
   Theoretical condition for which DNAPL
            infiltrates the fracture
Infiltration takes place if Dr g H exceeds the
  “fracture entry pressure” PE
                                      For a circular fracture of
       Water                            average radius r,
                   q                    PE = 2 s cos q / r
                                        s interfacial tension
    DNAPL Pool


                                        q contact angle

               r
                       INEEL Workshop, 2003
              Infiltration Criterion

                                              DrgHc = 2 s cos q / r

    Water
                                               Hc = 2 s cos q /Drg r
DNAPL Pool   q              H
                                             HC , critical height

         r

   Note: So far, all scaling relationships are known (H is
reduced by n, g is increased by n, r does not change and all
          other parameters are assumed invariant

                      INEEL Workshop, 2003
    Interface displacement during infiltration
       Field Scenario                  Experimental Modeling




H
                                           H
     Z(T)                                                  O

L
                                                           Z(T)
                                               L


                                                        simulated
                 e                                      fracture

                        INEEL Workshop, 2003
Interface displacement during infiltration

                               Change of momentum of
                                   fluid in fracture
                                           =
                                     Body forces
   H                                       
                O
                                    Viscous forces

                Z(T)                         
    L                                 Capillary forces
                                            
                                      End drag forces

               INEEL Workshop, 2003
     Interface displacement during infiltration

 Momentum conservation no end-drag

                 1            dZ              d 2 Z 2s cosq
0  D rg(H  Z)  mwl  DmZ   r wl  Dr Z 2 
                 ki           dT              dT       r

   By Inspectional Analysis the scale factor for ALL terms must by 1
              (DrgH is the same in model and prototype)


       Obtain an analytical solution by neglecting acceleration terms
   (inertia forces), assuming Dm = 0 and capillary forces (scosq) do not
                             change with time

                             INEEL Workshop, 2003
           Interface Displacement Equation
   Negligible Inertia Constant Contact Angle, q
   (NICCA Model)                                             H

         Z       Z  DH 
                                                                        O

             KD
         T       L                                        L
                                                                        Z



with    KD  kiDrg/ mw

    DH, difference between critical pool height and pool height (H-Hc)
   - KD, equivalent hydraulic conductivity of a fluid of density Dr and
              viscosity mw
    ki, intrinsic permeability of fracture (e2/32 for circular apertures)

                             INEEL Workshop, 2003
         Derived Scaling Relationships
                           Prototype                         Model
Macroscopic Dimensions    H, HC , Z, L             h=H/n, z=Z/n, l = L/N etc...
Microscopic Dimensions         r                               r
        Time                  T                             t=T/n2




         H
                                                              z(t)
                                            h                        r   ng
                                                      l
                   Z(T)
          L

               r                                                              rw
                     g


                            INEEL Workshop, 2003
   Experimental Setup Prior to Testing

                                                                           h




                                                                           l



Miniature
                                                       Glass-fronted box
camera
            1.0 m radius balanced arm centrifuge       filled with water
                   with swinging platform
                                INEEL Workshop, 2003
             Modeling-of-Models

If the modeling approach is correct:
      A 10 g test on a fracture l =20 cm (“prototye”
              length, L= 10 x 20 = 200 cm)
                should be equivalent to
           A 20 g test on a fracture l =10 cm
       (“prototye” length L = 20 x 10 = 200 cm)



                     INEEL Workshop, 2003
Modeling-of-Models 0.6 mm Capillary tubes
                                           0
  Depth of Prototype Interface, z [mm]


                                          200


                                          400
                   [mm]
                      Z




                                          600
                                                    Laboratory Test
                                                    l = 1201 mm
                                          800       Centrifuge Tests at N = 10
                                                    l = 119 mm
                                                    invasion at 9.7g
                                         1000
                                                    l = 119 mm
                                                    invasion at 10.4g
                                         1200

                                                0     100       200        300   400   500

                                                            Prototype Time, t T [s]
                                                                              [s]

                                                         INEEL Workshop, 2003
Modeling-of-Models1.3 mm capillary tubes
                                            0
   Depth of Prototype Interface, z [mm]
                              [mm]
                                          100       Is it due to
                                 Z



                                                      inertia?
                                          200


                                          300
                                                     Laboratory Test
                                                     l = 610 mm
                                          400
                                                     Centrifuge Test at N = 5
                                                     l = 120 mm invaded at 4.6g
                                          500        Centrifuge Test at N = 10
                                                     l = 60 mm invaded at 9.5g
                                          600        Centrifuge Test at N = 15
                                                     l = 40 mm invaded at 11.7g

                                                0         20        40        60     80   100

                                                               Prototype Time, t T [s]
                                                                                 [s]
                                                          INEEL Workshop, 2003
Initial Conclusions Modeling-of-Models
Theoretical model suggests that inertia is only negligible if

                   D rr w gki
                             2

                               1
                      mw l
                        2




As g increases the effects of inertia become more
important (and different for every test).

This explains some of the disagreement…...




                        INEEL Workshop, 2003
        Physical Model Tests
Performed 100 centrifuge model tests to
  investigate DNAPL infiltration into vertical
  fractures for conditions where inertia was
  negligible




                  INEEL Workshop, 2003
                 Predicting DNAPL infiltration (cos q = 1)
                     Laboratory tests (n = 1)                                         Centrifuge tests
                      (circular tubes only)                                         n=1.8 to 15.8 (4-CT)
                                                                            0
                                                                            0
                                                                            6
             0
             0
             4
                                o T Cl
                                r
                               b r s -lo n
                               a oe 4ou
                               Ltyt nhoe
                                a  so   t
                                       r e                                  5
                                                                            0
                                                                            5               u l
                                                                                           c ir l b
                                                                                           rap T
                                                                                           i l aru
                                                                                           C C ye
                                                                                                a s
             0
             5
             3                  r
                               b r s , -co e
                               Ltyt n1 h tn
                               a oe 1T rh
                                a   o
                                   s , ioa
                                o T 1rl e                                                   a r l
                                                                                             n
                                                                                           egC ye
                                                                                           Rua ru
                                                                                           c l p T
                                                                                            t a ia s
                                                                                                 l b




                                                        HC[m]
                                                                            0
                                                                            0
                                                                            5
             0
             3
             0                                                              0
                                                                            5
                                                                            4
                                                                            0
                                                                            0
                                                                            4
             5
             0
             2
hC[m]



                                 rc o
                                 ei n
                                  dne
                                  io
                                 Pt Z                                       5
                                                                            0
                                                                            3
             0
             0
             2                                                              3
                                                                            0
                                                                            0                 dne
                                                                                             ei n
                                                                                             rc o
                                                                                             Pt Z
                                                                                              io
                                                                            5
                                                                            0
                                                                            2
             5
             0
             1
                                                                            0
                                                                            0
                                                                            2
             0
             0
             1                                                              5
                                                                            0
                                                                            1
CritcalHeight,




                 0
                 5

                 0
                                                        ProtypeCritcalHeight,
                                                                            1
                                                                            0
                                                                            0
                                                                                0
                                                                                5
                                                                                0

                      .
                      5 .
                        0 .
                          5 .
                            0 .
                              5 .
                                0
                      0 1 1 2 2 3                                               0 0 1 1 2 2 3
                                                                                .
                                                                                0 .
                                                                                  5 .
                                                                                    0 .
                                                                                      5 .
                                                                                        0 .
                                                                                          5 .
                                                                                            0
                        C yem[ ]
                        a r u i ed
                        p T ae m
                         i
                         l
                         l b t
                          a  Dr m,                                                  Cyee , [ ]
                                                                                    a r upem
                                                                                    pT r d
                                                                                    il
                                                                                     l b t
                                                                                     a A  u m
                                                                                          r
                                                INEEL Workshop, 2003
  Initial Conclusions on Predicting Pool Height for
                 DNAPL Infiltration

Predicted values of critical pool height (Hc) offer
  reasonable agreement with scaled centrifuge data
  (generally upper-bound)
Scatter
   due to cleanliness of tube?
   Cos q <1?
   Something else?



                       INEEL Workshop, 2003
                                  Predicting Interface Displacement
                                        Tests in 2.7 mm tubes
                                                                              NICCA       Z       Z  DH 
                                                                                              KD
                                  0.0

                                                                                                   L 
 Interface Relative Depth, zc/l




                                  0.2
                                                                          l = 1202 mm
                                                                          l = 909 mm
                                                                                          T
                                                                          l = 606 mm
                                                                          l = 301 mm
                                  0.4                                     l = 103 mm
Z/L




                                                                          l = 88 mm
                                  0.6


                                  0.8


                                  1.0

                                        0   20   40   60   80     100   120   140   160

                                    Interface Corrected Velocity, (lt/l)dzc/dt [mm/s]
 Interface Velocity dZ/dT, mm/s
                                                                INEEL Workshop, 2003
Two “New” Mechanisms Influencing DNAPL
              Behavior
Contact Angle is dependent on velocity
                                               Wetting fluid
                                          displacing non-wetting
                                                   fluid
               Non-wetting fluid
            displacing wetting fluid


    q




                        INEEL Workshop, 2003
Interface Pinning at Low Velocities


             DNAPL                       Water



              Pinning force
             adds resistance                   Pinning at
                                              contact point




                       INEEL Workshop, 2003
       Revised Theoretical Model
New invasion/ infiltration criteria
          2s cosq s 2np fp
     Hc           
           Drgr      D rgr                  function of r


  dZ KD       2s cosq s 2s cosq 2np f p
        (Z                          )
  dt   L        Drgr     D rgr   Drgr



                     INEEL Workshop, 2003
                         Summary
Geocentrifuge used to generate an extensive set of
  data describing DNAPL infiltration into simple
  vertical fractures
Modeling-of-models used to define limits of derived
  scaling relationships
Comparison of centrifuge data with theoretical
  model used to improve model
Wouldn‟t have been possible in real and/ or complex system or at reduced
                             laboratory scale
                           INEEL Workshop, 2003
                Conclusions
Geocentrifuge has unique advantages when
  investigating subsurface transport
Both limitations and advantages of geo-centrifuge
  have to be defined for any problem
Investigation/ identification of fundamental
  processes and model validation key applications
  for centrifuge testing


                   INEEL Workshop, 2003

				
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