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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