Environmental Geomechanics and Transport Processes

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Environmental Geomechanics and Transport Processes

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

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Outline of Presentation

• Centrifuge Testing
• Uses of Geocentrifuge
• Scaling Relationships
• Limitations
• Example Study
• Conclusions

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Centrifuge Testing

• Two basic uses of geocentrifuge
• 1. Simulation of a prototype event
• 2. Investigation of system behavior

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Principle of Centrifuge Testing

• Use centrifugal acceleration to simulate
  gravitational acceleration

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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

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1. Traditional Use

• Physical modeling of a specific problem (the
  prototype)

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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

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Fluid Behavior Dependent Upon Pressure
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• 2. Body (gravitational) forces are important to
  the problem
• E.g., Fluids of contrasting density interacting,
  or vadose zone behavior

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Subsurface DNAPL Transport
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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

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Mathematical Models full, simplified
Direct modeling of prototype
Learn mechanism of transport processes Verificati
on/ Improvement of theory
Prototype actual field problem
Scale Physical Model centrifuge model
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2. Alternative Use

• Investigation of system behavior over range of
  conditions

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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

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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

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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)

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Deriving Scaling Relationships

• Partial inspectional analysis
• Dimensional analysis
• Both require some knowledge of processes
  important to the problem

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Validating Scaling Relationships

• Use technique of modeling of models - scaled
  centrifuge test data is compared to prototype
  data
• Very Important to ALL Model Testing

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Interesting Pressures

• Pressure Prototype/ Model Ratio
• Hydrostatic rgz 1
• Seepage vmz/r2 1
• Capillary 2scosq/r 1
• Body Drgz 1

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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

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What is Not Possible

• Acceleration of real-time-processes
• E.g., radioactive decay, microbial decay, NAPL
  dissolution, etc.
• Duplication of complexity found in field

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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

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• Centrifuge has proven very advantageous in
  investigating physical mechanisms of fluid and
  contaminant transport in controlled systems

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Example Study
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DNAPL Behavior in Fractures
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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

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Physics of the Problem
H
L
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Condition Before DNAPL infiltrates the fracture

• 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

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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 average radius r, PE
2 s cos q / r s interfacial tensionq
contact angle
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Infiltration Criterion
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
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Interface displacement during infiltration
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Interface displacement during infiltration
Change of momentum of fluid in fractureBody
forces ? Viscous forces ? Capillary forces ?
End drag forces
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Interface displacement during infiltration
Momentum conservation no end-drag
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
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Interface Displacement Equation
Negligible Inertia Constant Contact Angle, q
(NICCA Model)
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)
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Derived Scaling Relationships
Model hH/n, zZ/n, l L/N etc... r tT/n2
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Experimental Setup Prior to Testing
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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)

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Modeling-of-Models 0.6 mm Capillary tubes
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Modeling-of-Models1.3 mm capillary tubes
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Initial Conclusions Modeling-of-Models
Theoretical model suggests that inertia is only
negligible if
As g increases the effects of inertia become more
important (and different for every test). This
explains some of the disagreement...
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Physical Model Tests

• Performed 100 centrifuge model tests to
  investigate DNAPL infiltration into vertical
  fractures for conditions where inertia was
  negligible

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Predicting DNAPL infiltration (cos q 1)
Laboratory tests (n 1)(circular tubes only)
Pool Height (mm)
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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 lt1?
• Something else?

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Predicting Interface Displacement Tests in 2.7
mm tubes
NICCA
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Two New Mechanisms Influencing DNAPL Behavior
Contact Angle is dependent on velocity
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Interface Pinning at Low Velocities
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Revised Theoretical Model

• New invasion/ infiltration criteria

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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
• Wouldnt have been possible in real and/ or
  complex system or at reduced laboratory scale

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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