# Presentation: 103209

## An Efficient Reliability-Based Approach to Aquifer Remediation Design

- Howard W. Reeves
- U.S. Geological Survey
- Michigan District, Water Resources Discipline

- EPA Region 5 STAR Seminar
- July 14, 2004

## Acknowledgements

- U.S. Environmental Protection Agency (EPA) STAR Program through Grant R 827126-01-0
- Department of Civil Engineering, Northwestern University
- Co-PIs:  C.H. Dowding (Northwestern University) and T. Igusa (Johns Hopkins University)
- Colleagues and students:  A.J. Graettinger (University of Alabama), J. Lee (University of Missouri-Kansas City), M.D. Fortney (Law School at Northwestern U.), D. Dethan (ERM Consulting)

- Reeves - EPA Region 5 STAR Seminar

- July 14, 2004

## Motivating Problem

- Design of remedial strategies for contaminated soil and groundwater
- Uncertainties in site conditions
- Variety remedial options
- Desire to quantify design process

- Reeves - EPA Region 5 STAR Seminar

- July 14, 2004

## Challenges Given a contaminated site and proposed remedial activities:

- Geology of subsurface may be complex
- Small volume of soil at a site is sampled
- Parameters of interest may vary over large ranges
- Contaminants may have complex interactions with soil and native ground water
- Clean-up schemes impose different hydrologic, chemical, or biological conditions or constraints

- Reeves - EPA Region 5 STAR Seminar

- July 14, 2004

## Example 

- Cone Penetrometer
- (CPT) log

- CPT has an area of
- 10 cm2, but
- continuity of this
- layer  across the
- site is important

- Reeves - EPA Region 5 STAR Seminar

- July 14, 2004

## Heterogeneity

- at different scales

- Reeves - EPA Region 5 STAR Seminar

- July 14, 2004

## Reaction to Uncertainty

- Over design      -	leads to increased 					costs without 						improving 						performance

- Reeves - EPA Region 5 STAR Seminar

- July 14, 2004

## Reaction to Uncertainty

- Over design      -	leads to increased 					costs without 						improving 						performance
- Over sampling  -	increased cost 						without changing    					design

- Reeves - EPA Region 5 STAR Seminar

- July 14, 2004

## Site Characterization

- Are there sufficient data to base the design?
- What data are required and where should these data be collected to increase confidence in the design?

- Reeves - EPA Region 5 STAR Seminar

- July 14, 2004

## Approach

- Combine design model and geostatistical description of geologic setting to estimate *design uncertainty*
- Use *design uncertainty* to guide exploration
- Contrast with sampling based on budget or regulatory constraints

- Reeves - EPA Region 5 STAR Seminar

- July 14, 2004

## Hydrologic Decision 

- Investigation
- Program

- Geological
- Uncertainty
- Model

- Parameter
- Uncertainty
- Model

- Design
- Model

- Engineering
- Reliability
- Model

- Decision
- Model

- Hydrologic Decision
- Framework
- (Freeze *et al*., 1990)

- Reeves - EPA Region 5 STAR Seminar

- July 14, 2004

## Field

- Investigation
- Program

- Geological
- Uncertainty
- Model

- Parameter
- Uncertainty
- Model

- Design
- Model

- Engineering
- Reliability
- Model

- Decision
- Model

- Reeves - EPA Region 5 STAR Seminar

- July 14, 2004

## Slide 13

- Reeves - EPA Region 5 STAR Seminar

- July 14, 2004

## Input Component

- Bayesian approach to condition input vector, u, to observation vector, v
- Variance of u is the diagonal of C(u|v) matrix
- Can reduce to kriging estimate of E[u|v] with appropriate priors for E[u] and Cov(u)

- E[u|v] = E[u] + Cov(v,u) Cov(v)-1 (v - E[v])
- Cov(u|v) =  Cov(u) - Cov(v,u) Cov(v)-1 Cov(u,v)

- Reeves - EPA Region 5 STAR Seminar

- July 14, 2004

## First-Order Second-Moment

- E[C] ****  g( E[u|v] )

- Cov(C(t1),C(t2)) ****  Ju(to,t1) Cov(u|v) JuT (to,t2)

- E[C] = expected value for concentration
- g() = design model
- u = vector of uncertain input parameters
- Ju = [CI/  uJ ]
- Cov(.,.) = covariance matrix describing uncertainty in input parameters

- Reeves - EPA Region 5 STAR Seminar

- July 14, 2004

## Performance Evaluation

***Performance Evaluation***

**N(C,********c****)**

- Reeves - EPA Region 5 STAR Seminar

- July 14, 2004

## Point reliability may be determined

 c - the standard deviation of C = Square root of the variance of C

Uncertainty in site input and model performance are combined in C

-  c - the standard deviation of *C* = Square root of the variance of *C*
- Uncertainty in site input and model performance are combined in *C*

***Reliability Index***

- Reeves - EPA Region 5 STAR Seminar

- July 14, 2004

## Slide 18

- Reeves - EPA Region 5 STAR Seminar

- July 14, 2004

## 3-D Transport Simulation

**3-D Transport Simulation**

_**Hypothetical Model**_

- Reeves - EPA Region 5 STAR Seminar

- July 14, 2004

## 3-D Transport Simulation

- Steady state flow and transient transport
- - Uncertain input parameter -
- Geologic interface elevations : 4 samples
- First-order decay rate : 0.02 /day  0.005
- - Design parameter -
- 	    Design I : No pumping well (Natural Attenuation)
- 	    Design II : Single pumping well
- (Proposed pumping rate : 300 m3/day))
- - Output parameter -
- Clean-up goal at compliance point : 10-3 mg/L

_**Model Conditions and parameter description**_

- Reeves - EPA Region 5 STAR Seminar

- July 14, 2004

## Slide 21

- Reeves - EPA Region 5 STAR Seminar

- July 14, 2004

## Design I

- No Pumping Well

- Design II
- Single Pumping Well

- Reeves - EPA Region 5 STAR Seminar

- July 14, 2004

## Design I

- (mg2/L2)

- No Pumping Well

- Design II
- Single Pumping Well

- Total
- Variance

- Variance from
- Interface uncertainty

- Variance from
- First-order Decay rate
- uncertainty

- Reeves - EPA Region 5 STAR Seminar

- July 14, 2004

## Reliability index indicates which design is more reliable

- Reeves - EPA Region 5 STAR Seminar

- July 14, 2004

## Reliability index can be used to estimate probability of success

- Reeves - EPA Region 5 STAR Seminar

- July 14, 2004

## Will directed sampling give more confidence to the remedial design?

- _Directed Sampling_

- _Ad hoc Sampling_

**(mg****2****/L****2****)**

- _For Design I : No pumping well (Natural Attenuation)_

- Reeves - EPA Region 5 STAR Seminar

- July 14, 2004

## For Design I : No pumping well (Natural Attenuation)

- _For Design I : No pumping well (Natural Attenuation)_

- Reeves - EPA Region 5 STAR Seminar

- July 14, 2004

## For Design II : Single pumping well

- _For Design II : Single pumping well_

- _4 Sample_

- _6 Sample_

- Reeves - EPA Region 5 STAR Seminar

- July 14, 2004

## Additional sampling reduces the concentration uncertainty

- _6 Sample_

- _For Design II : Single pumping well_

- (mg2/L2)

- Reeves - EPA Region 5 STAR Seminar

- July 14, 2004

## For Design II : Single pumping well

- _For Design II : Single pumping well_

- Reeves - EPA Region 5 STAR Seminar

- July 14, 2004

## Future Work

- Approach incorporated with other design models (Dowding - NU, Graettinger - UA)
- Incorporate use of geophysical data for input (Lee - UMKC)
- Incorporate techniques into comprehensive modeling approach that includes model calibration and other uncertainty issues (Reeves - USGS)
- Test with field data and designs (All)

- Reeves - EPA Region 5 STAR Seminar

- July 14, 2004

## Bibliography (STAR + Related)

- Dowding, C.H., Reeves, H.W., Graettinger, A.J., and Lee, J., 2000, Inclusion of the Performance Model to Direct and Control Site Characterization, *in *Mayne, P.W. and Hyrciw, R.D., eds., Innovations and Applications in Geotechnical Site Characterization: Geo-Institute of the American Society of Civil Engineers, Geotechnical Special Publication Number 97, Reston, Virginia, ASCE, p. 130-141.
- Reeves, H.W., Lee, J., Dowding, C.H., and Graettinger, A.J., 2000, Reliability-Based Evaluation of Groundwater Remediation Strategies, *in *Stauffer, F., Kinzelbach, W., Kovar, K., and Hoehn, E., eds., Calibration and Reliability in Groundwater Modelling–Coping with Uncertainty, Proceedings of the ModelCARE ’99 Conference, Z ̈urich, September, 1999: IAHS Publication no. 265, Wallingford, Oxfordshire, UK, IAHS Press, p. 304-309.
- Fortney, M.D., 2001, Reliability Analysis for Groundwater Modeling using MODFLOW-2000: M.S. Thesis, Northwestern University, Evanston, Illinois, 114 p.
- Lee, J., 2001, Reliability-Based Approach for Groundwater Remediation Design:  Ph.D. Dissertation, Northwestern University, Evanston, Illinois, 161 p.
- Graettinger, A.J., Lee, J., and Reeves, H.W., 2002, Efficient Conditional Modeling for Geotechnical Uncertainty Evaluation: International Journal for Numerical and Analytical Methods in Geomechanics, v. 26, no. 2, p. 163-179.
- Lee, J., Reeves, H.W., and Dowding, C.H., 2002, Integrating Site Characterization with Aquifer and Soil Remediation Design *in *Lipnick, R.L., Mason, R.P., Phillips, M.L., and Pittman, C.U., Jr., eds., Fate and Transport of Chemicals in the Environment: Impacts, Monitoring, and Remediation, ACS Symposium Series 806: Washington, D. C., American Chemical Society, p. 384-396.
- Glasgow, H.S., Fortney, M.D., Lee, J., Graettinger, A.J., and Reeves, H.W., 2003, MODFLOW-2000 Head Uncertainty, A First-Order Second-Moment Method: Ground Water, v. 41, no. 3, p. 342-350.
- Graettinger, A.J., Reeves, H.W., Lee, J., and Dethan, D., 2003, First-Order Second-Moment Site Exploration Approaches, Mishra, S., ed., Groundwater Quality Modeling and Management Under Uncertainty Proceedings of the Probabilistic Approaches & Groundwater Modeling Symposium held during the World Water and Environmental Resources Congress in Philadelphia, Pennsylvania, June 24-26, 2003: Washington, D.C., American Society of Civil Engineers, p. 215-225.

- Reeves - EPA Region 5 STAR Seminar

- July 14, 2004

## Thank you

- R 827126-01-0

*Thank you*

- Reeves - EPA Region 5 STAR Seminar

- July 14, 2004