Utilizing Image Analysis for Variable-Density Flow Benchmarking Datasets

1. Use of Image Analysis to develop new benchmarking datasets for variable-density flow scenarios Rohit R. Goswami1,2, and T. Prabhakar Clement1 1 Department of Civil Engineering, Auburn University, Auburn, AL 2Geosyntec Consultants, Boca Raton, FL

2. Outline • Components of Image Analysis (IA) procedure • Overview of IA • Benchmarking experiments • Two experiments- rising plume, sinking plume • Numerical modeling • Challenges • Alternate approaches

3. Image Analysis- Background • Goswami & Clement (2007)- Laboratory-scale investigation of saltwater intrusion dynamics- Water Resources Research (43) Advancing Saltwater Wedge 5 mins 15 mins 55 mins

4. Components of IA • Calibration Relationship: fluid property v/s image property • Calibration data- experimentally obtained • Regression analysis- selecting relationship • Estimation of concentration levels 0.0 0.5 1.0 2.0 3.0 4.0

5. Benchmarking • Popular benchmarks • Henry problem- Henry (1964), Simpson & Clement (2004) • Elder problem- Elder (1967), Voss & Souza (1987) • Recent benchmarks- stable case • Oswald & Kinzelbach (2004), Goswami & Clement (2007) • Unstable case • Salt lake problem • Instabilities • Concentration data ? • Proposed exercise • IA to obtain concentration data • Testing the numerical approach

6. Flow Tank Lighting CCD Camera Translucent Sheet Variable-density Experiments • Laboratory Setup • 6 MP CCD Camera • CFL bulbs • LTM • Porous media • Homogeneous packing • Image analysis process • Two experiments- rising plume, sinking plume LTM

7. Variable-density Experiments • Example flow-tank setup

8. Physical Model- Rising Plume 0 min 3 min 6 min 8 min

9. Physical Model- Sinking Plume 0 min 2 min 5 min

10. z x Conceptualization- Rising Plume p=0 p=0 Porous Media 180 mm 153 mm injection point 114 mm 225 mm

11. z x Conceptualization- Sinking Plume constant h 174 mm constant h 178 mm injection point 54 mm Porous Media 145 mm 225 mm

12. Numerical Modeling • Generation of instabilities- two approaches • Use of particle-tracking methods (MOC) with low dispersivity values • Use small scale heterogeneities • Which approach is appropriate and why? • We will explore both approaches using the variable-density model SEAWAT

13. MOC Results- Rising

14. MOC Results- Sinking

15. Heterogeneity Generation Flow Tank TUBA MATLAB 1% variability

16. Heterogeneity Results 0 min 1.0% Variability 3 min 0 min 2 min 5 min 6 min 8 min 1% Variability

17. How Much Heterogeneity? 0 min 3 min 6 min 8 min 0.1% Variability 10% Variability 1.0% Variability

18. Summary • Benchmarking datasets • We propose to use a combination of two unstable problems involving a sinking and a rising plume • They offer a unique combination – one with unstable fingers and one without fingers • Unstable benchmark problems can be simulated using two approaches – which is appropriate? • MOC/TVD with low dispersivity values • Heterogeneities • Heterogeneity approach appears to be more appropriate • How much heterogeneity to use is an open question

19. Acknowledgements • Mr. Bharath Ambale, PhD Candidate, Department of Electrical Engineering, Auburn University • Dr. Elena Abarca, Fulbright Fellow, MIT, formerly at Auburn University • Mrs. Linzy Brakefield, USGS, formerly at Auburn University • Department of Civil Engineering, Auburn University, AL • Geosyntec Consultants, Boca Raton, FL

20. Discussion