an efficient reliability-based approach to aquifer remediation design howard w. reeves u.s....

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 SeminarJuly 14, 2004

July 14, 2004 Reeves - EPA Region 5 STAR Seminar 2

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)

July 14, 2004 Reeves - EPA Region 5 STAR Seminar 3

Motivating Problem

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

July 14, 2004 Reeves - EPA Region 5 STAR Seminar 4

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

July 14, 2004 Reeves - EPA Region 5 STAR Seminar 5

Example Cone Penetrometer(CPT) log

CPT has an area of10 cm2, but continuity of this layer across thesite is important

July 14, 2004 Reeves - EPA Region 5 STAR Seminar 6

Heterogeneityat different scales

July 14, 2004 Reeves - EPA Region 5 STAR Seminar 7

Reaction to Uncertainty

• Over design - leads to increased costs without

improving

performance

July 14, 2004 Reeves - EPA Region 5 STAR Seminar 8

Reaction to Uncertainty

• Over design - leads to increased costs without improving performance

• Over sampling - increased cost without changing design

July 14, 2004 Reeves - EPA Region 5 STAR Seminar 9

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?

July 14, 2004 Reeves - EPA Region 5 STAR Seminar 10

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

July 14, 2004 Reeves - EPA Region 5 STAR Seminar 11

FieldInvestigation

Program

GeologicalUncertainty

Model

ParameterUncertainty

Model

DesignModel

EngineeringReliability

Model

DecisionModel

Hydrologic Decision Framework (Freeze et al., 1990)

July 14, 2004 Reeves - EPA Region 5 STAR Seminar 12

FieldInvestigation

Program

GeologicalUncertainty

Model

ParameterUncertainty

Model

DesignModel

EngineeringReliability

Model

DecisionModel

July 14, 2004 Reeves - EPA Region 5 STAR Seminar 13

Performance Model

m

Performance Evaluation

m

P

Goal

Design Proposal and

Data Acquisition

Design Model Performance

Performance

Uncertainty

Evaluation of Design

and Performance

Reliability

Bayesian Condition

al Calculation

MODFLOW- 2000

First-Order

Second Moment (FOSM) Method

Reliability

Index,

Analysis

Sensitivity

Analysis

Sensitivity- Equation

Sensitivities

Input Parameter Model

Finite Element/

Performance Uncertainty

Design & Data

Sampling

Input parameter model

July 14, 2004 Reeves - EPA Region 5 STAR Seminar 14

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)

Input parameter model

July 14, 2004 Reeves - EPA Region 5 STAR Seminar 15

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 concentrationg() = design model u = vector of uncertain input parametersJu = [CI/ uJ ] Cov(.,.) = covariance matrix describing uncertainty in input parameters

Performance Uncertainty

July 14, 2004 Reeves - EPA Region 5 STAR Seminar 16

C

c

Ca

Probability of Success

Performance Evaluation

m

P

Goal Performance Evaluation

N(C,c)

July 14, 2004 Reeves - EPA Region 5 STAR Seminar 17

• 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

Reliability Index

= Ca - C

c

Performance Evaluation

m

P

Goal

July 14, 2004 Reeves - EPA Region 5 STAR Seminar 18

Case 1

Case 2

2

1

E[C] 2 E[C] 1

Probability of Failure for Case 2

Probability of Failure for Case 1

Performance Goal

Performance Evaluation

m

P

Goal

July 14, 2004 Reeves - EPA Region 5 STAR Seminar 19

0 1000-60

-50

-40

-30

-20

-10

0

0 10 20 30 40 (mg/L)

Kx=Ky=Kz=0.0004 n=0.66

Kx=Ky=Kz=4 n=0.33

Kx=Ky=Kz=0.0004 n=0.66

Clay

Clay

Sand

Z

X

K : conductivity (m/day), n : porosity

0 10000

1000

flow

No flow boundary

No flow boundary

h=50m

Y

X

h=40m

(UNIT=m)

Sampling location

Proposed pumping well

Compliance point

3-D Transport Simulation

Hypothetical Model

Date Sampling

July 14, 2004 Reeves - EPA Region 5 STAR Seminar 20

3-D Transport Simulation

Steady state flow and transient transport

- Uncertain input parameter -Geologic interface elevations : 4 samplesFirst-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

July 14, 2004 Reeves - EPA Region 5 STAR Seminar 21

0.00.40.81.21.62.02.42.8

(m )

Dep

th, Z

(m

)

Input parameter model

July 14, 2004 Reeves - EPA Region 5 STAR Seminar 22

Performance Model

m

0 500 1000

X (m )

-60

-40

-20

0

De

pth

, Z (

m)

0 500 1000

X (m )

-60

-40

-20

0

De

pth

, Z (

m)

01234567

0 500 1000

X (m )

-60

-40

-20

0

De

pth

, Z (

m)

0

10

20

30

40

(m g/L)

Aquifer boundaries

(m g/L)

Design INo Pumping Well

Design IISingle Pumping Well

July 14, 2004 Reeves - EPA Region 5 STAR Seminar 23

0.00.20.40.60.81.01.21.4

0.00

0.04

0.08

0.12

0.16

0.20

0.00.20.40.60.81.01.2

0.00.40.81.21.62.02.42.83.2

0.00.40.81.21.62.02.42.83.2

0.000

0.002

0.004

0.006

0.008

0.010

(mg2/L2)

Design INo Pumping Well

Design IISingle Pumping Well

TotalVariance

Variance from Interface uncertainty

Variance from First-order Decay rate

uncertainty

Performance Uncertainty

July 14, 2004 Reeves - EPA Region 5 STAR Seminar 24

Reliability index indicates which design is more reliable

0

10

20

30

40

50

60

70

0 50 100 150 200 250 300 350

Time(days)

Design I

Design II

Performance Evaluation

m

P

Goal

July 14, 2004 Reeves - EPA Region 5 STAR Seminar 25

54.3061

100.000099.6825

99.9996 100.0000

65.4521

0

20

40

60

80

100

0 50 100 150 200 250 300 350Time (days)

x 1

00 (%

)

Design I

Design II

Performance Evaluation

m

P

GoalReliability index can be used to estimate probability of success

July 14, 2004 Reeves - EPA Region 5 STAR Seminar 26

0 1000

X(m )

0

1000

Y(m

)

0.00.20.40.60.81.01.21.4

0 1000

X(m )

0

1000

Y(m

)

0.00.20.40.60.81.01.21.4

Directed Sampling Ad hoc Sampling

(mg2/L2)

Will directed sampling give more confidence to the remedial design?For Design I : No pumping well (Natural Attenuation)

Performance Uncertainty

July 14, 2004 Reeves - EPA Region 5 STAR Seminar 27

0.10

0.11

0.12

0.13

3 4 5 6 7

Number of samples

directed sampling

ad hoc sampling

For Design I : No pumping well (Natural Attenuation)

Performance Evaluation

m

P

Goal

July 14, 2004 Reeves - EPA Region 5 STAR Seminar 28

De

pth

, Z

(m

)

De

pth

, Z

(m

)

(m )-4.0 -2.0 0.0 2.0

Input parameter model

For Design II : Single pumping wellAdditional Sampling

4 Sample 6 Sample

July 14, 2004 Reeves - EPA Region 5 STAR Seminar 29

4 Sample 6 Sample

Additional sampling reduces the concentration uncertainty

For Design II : Single pumping well

0 1000

X (m )

0

1000

Y (

m)

0 1000

X (m )

0

1000

Y (

m)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

S 5

S 6S 7

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

Performance Uncertainty

(mg2/L2)

July 14, 2004 Reeves - EPA Region 5 STAR Seminar 30

68.3880

65.4521

60

65

70

3 4 5 6 7

Number of samples

x 1

00 (

%)

Performance Evaluation

m

P

Goal

For Design II : Single pumping well

July 14, 2004 Reeves - EPA Region 5 STAR Seminar 31

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)

July 14, 2004 Reeves - EPA Region 5 STAR Seminar 32

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.

July 14, 2004 Reeves - EPA Region 5 STAR Seminar 33

R 827126-01-0

Thank you