# Presentation: 266957

## 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

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## Result

- ( g z)prototype = ( *n*g z/*n*) model
-  = 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

- INEEL Workshop, 2003

- Verification/ Improvement of theory

**Mathematical Models**
** ****[full, simplified]**

**Scale Physical Model **
**[centrifuge model]**

**Prototype**
**[actual field problem]**

- Direct modeling
- of prototype

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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

- 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

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## Often Assumed Relationships

**Parameter****	****	****Protoype/ Model Ratio**
- Intrinsic Permeability, k		1	 n = Scaling Factor
- Fluid Viscosity, Density,
- 	Interfacial Tension 	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 		gz		1
- Seepage		 vz/r2	1
- Capillary	 	2cosr	1
- Body		 	gz		1

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## Dimensionless Numbers

**Number****	****	****	****	****Prototype/ Model Ratio**
- Re 		(vd/)		1/n	d = micro
- Pe 		(vd/Dd)		1/n	L = macro
- Ca(micro) 	(v/)		1/n
- Bo(micro) 	(gd2/)		1/n
- Ca(macro) 	(vL/d)		1
- Bo(macro) 	(gdL/)		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

*L*

*H*

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## Condition Before DNAPL infiltrates the fracture

- The static pressure difference at the DNAPL-water interface is equal to ***g H* where **is the density contrast between water and DNAPL

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## Theoretical condition for which DNAPL infiltrates the fracture

- Infiltration takes place if ***g H* exceeds the “fracture entry pressure” *P**E*

- For  a circular fracture of average radius *r*, PE = 2 ** cos ** / *r* *** * interfacial tension**  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 fracture=Body forces  Viscous forces
-  Capillary forces
-  End drag forces

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## Interface displacement during infiltration

- Momentum conservation no end-drag

- Obtain an analytical solution by neglecting acceleration terms (inertia forces), assuming  = 0 and capillary forces (cos) do not change with time

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

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## Interface Displacement Equation

- with

- *H*, difference between critical pool height and pool height (H-Hc)
- - *K*, equivalent hydraulic conductivity of a fluid of density and 		viscosity ***w*
- ki,intrinsic permeability of fracture (e2/32 for circular apertures)

- Negligible Inertia Constant Contact Angle,  (NICCA Model)

*K* ki*g/ ****w*

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## Derived Scaling Relationships

- Model
*h=H/n, z=Z/n, l = L/N *etc...* r **t=T/n*2

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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  = 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  <1?
- 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
- 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