Efficient sampling techniques for uncertainty quantification in history matching using nonlinear error models and ensemble level upscaling techniques

Handle URI:
http://hdl.handle.net/10754/598116
Title:
Efficient sampling techniques for uncertainty quantification in history matching using nonlinear error models and ensemble level upscaling techniques
Authors:
Efendiev, Y.; Datta-Gupta, A.; Ma, X.; Mallick, B.
Abstract:
The Markov chain Monte Carlo (MCMC) is a rigorous sampling method to quantify uncertainty in subsurface characterization. However, the MCMC usually requires many flow and transport simulations in evaluating the posterior distribution and can be computationally expensive for fine-scale geological models. We propose a methodology that combines coarse- and fine-scale information to improve the efficiency of MCMC methods. The proposed method employs off-line computations for modeling the relation between coarse- and fine-scale error responses. This relation is modeled using nonlinear functions with prescribed error precisions which are used in efficient sampling within the MCMC framework. We propose a two-stage MCMC where inexpensive coarse-scale simulations are performed to determine whether or not to run the fine-scale (resolved) simulations. The latter is determined on the basis of a statistical model developed off line. The proposed method is an extension of the approaches considered earlier where linear relations are used for modeling the response between coarse-scale and fine-scale models. The approach considered here does not rely on the proximity of approximate and resolved models and can employ much coarser and more inexpensive models to guide the fine-scale simulations. Numerical results for three-phase flow and transport demonstrate the advantages, efficiency, and utility of the method for uncertainty assessment in the history matching. Copyright 2009 by the American Geophysical Union.
Citation:
Efendiev Y, Datta-Gupta A, Ma X, Mallick B (2009) Efficient sampling techniques for uncertainty quantification in history matching using nonlinear error models and ensemble level upscaling techniques. Water Resour Res 45: n/a–n/a. Available: http://dx.doi.org/10.1029/2008WR007039.
Publisher:
Wiley-Blackwell
Journal:
Water Resources Research
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
Nov-2009
DOI:
10.1029/2008WR007039
Type:
Article
ISSN:
0043-1397
Sponsors:
We would like to acknowledge partial support from NSF grant CMG 0724704. This work is partly supported by award KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). We thank the reviewers for their comments that helped to improve the paper.
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Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorEfendiev, Y.en
dc.contributor.authorDatta-Gupta, A.en
dc.contributor.authorMa, X.en
dc.contributor.authorMallick, B.en
dc.date.accessioned2016-02-25T13:12:59Zen
dc.date.available2016-02-25T13:12:59Zen
dc.date.issued2009-11en
dc.identifier.citationEfendiev Y, Datta-Gupta A, Ma X, Mallick B (2009) Efficient sampling techniques for uncertainty quantification in history matching using nonlinear error models and ensemble level upscaling techniques. Water Resour Res 45: n/a–n/a. Available: http://dx.doi.org/10.1029/2008WR007039.en
dc.identifier.issn0043-1397en
dc.identifier.doi10.1029/2008WR007039en
dc.identifier.urihttp://hdl.handle.net/10754/598116en
dc.description.abstractThe Markov chain Monte Carlo (MCMC) is a rigorous sampling method to quantify uncertainty in subsurface characterization. However, the MCMC usually requires many flow and transport simulations in evaluating the posterior distribution and can be computationally expensive for fine-scale geological models. We propose a methodology that combines coarse- and fine-scale information to improve the efficiency of MCMC methods. The proposed method employs off-line computations for modeling the relation between coarse- and fine-scale error responses. This relation is modeled using nonlinear functions with prescribed error precisions which are used in efficient sampling within the MCMC framework. We propose a two-stage MCMC where inexpensive coarse-scale simulations are performed to determine whether or not to run the fine-scale (resolved) simulations. The latter is determined on the basis of a statistical model developed off line. The proposed method is an extension of the approaches considered earlier where linear relations are used for modeling the response between coarse-scale and fine-scale models. The approach considered here does not rely on the proximity of approximate and resolved models and can employ much coarser and more inexpensive models to guide the fine-scale simulations. Numerical results for three-phase flow and transport demonstrate the advantages, efficiency, and utility of the method for uncertainty assessment in the history matching. Copyright 2009 by the American Geophysical Union.en
dc.description.sponsorshipWe would like to acknowledge partial support from NSF grant CMG 0724704. This work is partly supported by award KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). We thank the reviewers for their comments that helped to improve the paper.en
dc.publisherWiley-Blackwellen
dc.titleEfficient sampling techniques for uncertainty quantification in history matching using nonlinear error models and ensemble level upscaling techniquesen
dc.typeArticleen
dc.identifier.journalWater Resources Researchen
dc.contributor.institutionDepartment of Mathematics; Texas A&M University; College Station; Texas; USAen
dc.contributor.institutionDepartment of Petroleum Engineering; Texas A&M University; College Station; Texas; USAen
dc.contributor.institutionDepartment of Statistics; Texas A&M University; College Station; Texas; USAen
kaust.grant.numberKUS-C1-016-04en
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