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

2 Geosyntec Consultants, Boca Raton, FL

Outline

Components of Image Analysis (IA) procedure

• Overview of IA

Benchmarking experiments

• Two experiments- rising plume, sinking plume

Numerical modeling

• Challenges

• Alternate approaches

Image Analysis- Background

Advancing Saltwater Wedge

5 mins 15 mins 55 mins

Goswami & Clement (2007)- Laboratory-scale investigation of saltwater intrusion dynamics- Water Resources Research (43)

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

4.03.0 2.0

1.00.5

BenchmarkingPopular 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

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

Variable-density Experiments

Example flow-tank setup

Physical Model- Rising Plume

0 min 3 min

6 min 8 min

Physical Model- Sinking Plume

0 min 2 min 5 min

Conceptualization- Rising Plume

225 mm

180 mm

114 mm injection point

Porous Media

p=0p=0

153 mm

x

z

Conceptualization- Sinking Plume

225 mm

54 mm

injection point

Porous Media145

mm

constant h 174 mm

constant h 178 mm

x

z

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

MOC Results- Rising

MOC Results- Sinking

Heterogeneity Generation

Flow Tank

TUBA MATLAB

1% variability

Heterogeneity Results

0 min 3 min

6 min 8 min

1.0% Variability

0 min 2 min 5 min

1% Variability

How Much Heterogeneity?

0 min 3 min

6 min 8 min

1.0% Variability

10% Variability0.1% Variability

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

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

Discussion