1. Céline Scheidt, Jef Caers and Philippe Renard
Annual Meeting 2012
Stanford Center for Reservoir Forecasting
The Ensemble project: a multi-disciplinary research effort for stochastic aquifer modeling
Céline Scheidt, Jef Caers and Philippe Renard

2. The ENSEMBLE Project Multi-disciplinary project: 6 universities
SCRF 2012

3. Project Overview (1/2) The aims of the ENSEMBLE project are:
Modeling groundwater systems requires developments in geology, physics, geophysics, hydrogeology, mathematics, …
Pursued independently by different teams
The aims of the ENSEMBLE project are:
Integrate recent developments in quantitative geology, hydrology, numerical, and stochastic modeling
Increase understanding of complex hydrological systems
Develop new methods for the characterization of alluvial systems
SCRF 2012

4. Project Overview (1/2)
Focus on common field sites corresponding to different alluvial systems (Tagliamento, Thur, Birs, Herten)
 used to illustrate and test the methods developed in the project
Herten site
Tagliamento site
SCRF 2012

5. Main Components of the Project
Source:

6. Subproject E: distance-based modeling
Conceptual uncertainty:
A data-constrained sensitivity analysis
Presentation given by Darryl Fenwick on Wednesday
Joint match of production data and GPR data
Use of distance-based methods
Definition of an accurate model of uncertainty with limited number of model evaluations
SCRF 2012

7. Motivation
Assumption: Inverse modeling improves the reliability of the predictions
The better the match, the better the model of uncertainty (in terms of predictions)
Is that necessarily true, especially for the type of problems encountered in hydrology?
Can we evaluate a relationship between the observed data and the prediction response?
Determine if matching the data improves the model of uncertainty
SCRF 2012

8. Illustrative Example – Aquifer Analog
TI – from Herten 5m
Injection of tracer
20m
Observation of tracer concentration at 3 depths
Prediction of tracer concentration
Observable data
3.5 days
Prediction data
12 days
Uncertainty ?
SCRF 2012

9. Model-Driven Inverse Modeling
PPM: Creation of 30 models matching the data
Prediction
2235 forward simulations for estimation of uncertainty
Goal: uncertainty on the tracer predictions.
Is it necessary to construct 30 HM models for this case?
SCRF 2012

10. Creation of 200 initial models
Problem Statement
Observable data
3.5 days
Creation of 200 initial models
Forward modeling
Prediction data
12 days
Relationship?
No inverse modeling performed
SCRF 2012

11. Creation of a Joint Space
Recap from Wednesday (J. Caers)
Creation of a joint space model-data (m*,d*)
m* and d* are obtained by using the first component of MDS
(m*,d*)  (d*,h*)
Use of the first component of the prediction h* instead of the models m* h*
Caers 2012
SCRF 2012

12. Joint Space (d*,h*)
Any dimensionality reduction technique can be used to construct (d*,h*)
NLPCA
PDF for h1*
d*obs
Large reduction of uncertainty in h1*
Observation response  d*
Prediction response  h*
SCRF 2012

13. Advantages of (d*,h*)
Comparison of prior/posterior distributions of h* indicates if inverse modeling allows for a better characterization of uncertainty
Can we beyond this diagnostic process?
Can we sample directly the posterior distribution to get new prediction curves?
SCRF 2012

14. Creation of New Responses
Observation response  d1*
Prediction response  h1*, h2*
d*obs
SCRF 2012

15. Comparison of Uncertainty
Matched concentration – depth 1
PPM
Rej. Samp.
NLPCA
Predicted concentration
P10-P90 interval
# simulations
Rej. Sampler
PPM
NLPCA
24,963
2,235
200

16. Summary
Different match of tracer concentration gives similar prediction
Purpose-driven inverse modeling is designed for cases where history matched models are not needed
Only interested in the response of the models that are available from the initial ensemble
Model-driven inverse modeling is required when models for multiple purposes are necessary
SCRF 2012

17. Future Work Preliminary results More tests should be performed
Initial number of simulations?
How many dimensions?
The more dimensions, the more precise the d*, h* relationship
However, the more dimensions, the more points are required to fill the space
Alternative dimensionality reduction techniques
SCRF 2012