Environmental Geomechanics and Transport Processes

1. Environmental Geomechanics and Transport Processes Patricia J. Culligan Department of Civil & Environmental Engineering, M.I.T INEEL Workshop, 2003

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

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

4. w r g rw2 = ng Prototype - full-scale Model - scale1/n Principle of Centrifuge Testing Use centrifugal acceleration to simulate gravitational acceleration INEEL Workshop, 2003

5. Result (r g z)prototype = (rng z/n) model r = density z = macroscopic length Similitude in stress/ pressure obtained between the scale model and the prototype INEEL Workshop, 2003

6. 100 m 1 m Water Pressure Strain Prototype Model at 100 g Data Point 1. Traditional Use Physical modeling of a specific problem (the ‘prototype’) INEEL Workshop, 2003

7. 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

8. Fluid Behavior Dependent Upon Pressure INEEL Workshop, 2003

9. 2. Body (gravitational) forces are important to the problem E.g., Fluids of contrasting density interacting, or vadose zone behavior INEEL Workshop, 2003

10. Subsurface DNAPL Transport INEEL Workshop, 2003

11. 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

12. Mathematical Models [full, simplified] Direct modeling of prototype Learn mechanism of transport processes Verification/ Improvement of theory Prototype [actual field problem] Scale Physical Model [centrifuge model] INEEL Workshop, 2003

13. Water Pressure 1 m 1 m 1 m 50 g 100 g 10 g Strain Same Model; different g-levels System Behavior 2. Alternative Use Investigation of system behavior over range of conditions INEEL Workshop, 2003

14. 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

15. 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

16. 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

17. Deriving Scaling Relationships Partial inspectional analysis Dimensional analysis Both require some knowledge of processes important to the problem INEEL Workshop, 2003

18. 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

19. Interesting Pressures Pressure Prototype/ Model Ratio Hydrostatic rgz 1 Seepage vmz/r2 1 Capillary 2scosq/r 1 Body Drgz 1 INEEL Workshop, 2003

20. 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

21. 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

22. 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

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

24. Example Study INEEL Workshop, 2003

25. Excavation, SVE Porous media Pump and treat, enhanced P&T, air sparging Plume control: feasibleAquifer cleanup: difficult Fractured media No known formula for successful remediation DNAPL Behavior in Fractures INEEL Workshop, 2003

26. 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

27. Experimental Modeling Field Scenario DNAPL pool H Reservoir tube Fracture initially saturated with water (under hydrostatic conditions) L Simulated fracture r e Physics of the Problem H L INEEL Workshop, 2003

28. Water DNAPL Water H DNAPL Pool Pressure DNAPL-water interface Static pressure difference 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 INEEL Workshop, 2003

29. Water q DNAPL Pool r 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 / rs interfacial tensionq contact angle INEEL Workshop, 2003

30. DrgHc = 2 s cos q / r Hc = 2 s cos q /Drg r Water q DNAPL Pool H HC , critical height r 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 INEEL Workshop, 2003

31. Field Scenario Experimental Modeling H H O Z(T) L Z(T) L simulated fracture e Interface displacement during infiltration INEEL Workshop, 2003

32. H O Z(T) L Interface displacement during infiltration Change of momentum of fluid in fracture=Body forcesViscous forces Capillary forces  End drag forces INEEL Workshop, 2003

33. 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 INEEL Workshop, 2003

34. H O Z L 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) INEEL Workshop, 2003

35. Prototype H, HC , Z, L r T Macroscopic DimensionsMicroscopic DimensionsTime z(t) H ng h r l Z(T) rw L r g Derived Scaling Relationships Model h=H/n, z=Z/n, l = L/N etc... r t=T/n2 INEEL Workshop, 2003

36. h l Miniature camera Glass-fronted box filled with water 1.0 m radius balanced arm centrifuge with swinging platform Experimental Setup Prior to Testing INEEL Workshop, 2003

37. 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

38. Z [mm] T [s] Modeling-of-Models 0.6 mm Capillary tubes INEEL Workshop, 2003

39. Z [mm] Is it due to inertia? T [s] Modeling-of-Models1.3 mm capillary tubes INEEL Workshop, 2003

40. 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…... INEEL Workshop, 2003

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

42. Centrifuge testsn=1.8 to 15.8 (4-CT) Predicting DNAPL infiltration (cos q = 1) Laboratory tests (n = 1)(circular tubes only) Pool Height (mm) INEEL Workshop, 2003

43. 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

44. Z/L Interface Velocity dZ/dT, mm/s Predicting Interface Displacement Tests in 2.7 mm tubes NICCA INEEL Workshop, 2003

45. Wetting fluid displacing non-wetting fluid Non-wetting fluid displacing wetting fluid q Two “New” Mechanisms Influencing DNAPL Behavior Contact Angle is dependent on velocity INEEL Workshop, 2003

46. DNAPL Water Pinning force adds resistance Pinning at contact point Interface Pinning at Low Velocities INEEL Workshop, 2003

47. function of r Revised Theoretical Model New invasion/ infiltration criteria INEEL Workshop, 2003

48. 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

49. 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