On the predictivity of pore-scale simulations: estimating uncertainties with multilevel Monte Carlo

Handle URI:
http://hdl.handle.net/10754/595933
Title:
On the predictivity of pore-scale simulations: estimating uncertainties with multilevel Monte Carlo
Authors:
Icardi, Matteo ( 0000-0003-3924-3117 ) ; Boccardo, Gianluca; Tempone, Raul ( 0000-0003-1967-4446 )
Abstract:
A fast method with tunable accuracy is proposed to estimate errors and uncertainties in pore-scale and Digital Rock Physics (DRP) problems. The overall predictivity of these studies can be, in fact, hindered by many factors including sample heterogeneity, computational and imaging limitations, model inadequacy and not perfectly known physical parameters. The typical objective of pore-scale studies is the estimation of macroscopic effective parameters such as permeability, effective diffusivity and hydrodynamic dispersion. However, these are often non-deterministic quantities (i.e., results obtained for specific pore-scale sample and setup are not totally reproducible by another “equivalent” sample and setup). The stochastic nature can arise due to the multi-scale heterogeneity, the computational and experimental limitations in considering large samples, and the complexity of the physical models. These approximations, in fact, introduce an error that, being dependent on a large number of complex factors, can be modeled as random. We propose a general simulation tool, based on multilevel Monte Carlo, that can reduce drastically the computational cost needed for computing accurate statistics of effective parameters and other quantities of interest, under any of these random errors. This is, to our knowledge, the first attempt to include Uncertainty Quantification (UQ) in pore-scale physics and simulation. The method can also provide estimates of the discretization error and it is tested on three-dimensional transport problems in heterogeneous materials, where the sampling procedure is done by generation algorithms able to reproduce realistic consolidated and unconsolidated random sphere and ellipsoid packings and arrangements. A totally automatic workflow is developed in an open-source code [2015. https://bitbucket.org/micardi/porescalemc.], that include rigid body physics and random packing algorithms, unstructured mesh discretization, finite volume solvers, extrapolation and post-processing techniques. The proposed method can be efficiently used in many porous media applications for problems such as stochastic homogenization/upscaling, propagation of uncertainty from microscopic fluid and rock properties to macro-scale parameters, robust estimation of Representative Elementary Volume size for arbitrary physics.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
On the predictivity of pore-scale simulations: estimating uncertainties with multilevel Monte Carlo 2016 Advances in Water Resources
Publisher:
Elsevier BV
Journal:
Advances in Water Resources
Issue Date:
8-Feb-2016
DOI:
10.1016/j.advwatres.2016.01.004
Type:
Article
ISSN:
03091708
Additional Links:
http://linkinghub.elsevier.com/retrieve/pii/S0309170816300045; https://bitbucket.org/micardi/porescalemc
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorIcardi, Matteoen
dc.contributor.authorBoccardo, Gianlucaen
dc.contributor.authorTempone, Raulen
dc.date.accessioned2016-02-09T13:30:04Zen
dc.date.available2016-02-09T13:30:04Zen
dc.date.issued2016-02-08en
dc.identifier.citationOn the predictivity of pore-scale simulations: estimating uncertainties with multilevel Monte Carlo 2016 Advances in Water Resourcesen
dc.identifier.issn03091708en
dc.identifier.doi10.1016/j.advwatres.2016.01.004en
dc.identifier.urihttp://hdl.handle.net/10754/595933en
dc.description.abstractA fast method with tunable accuracy is proposed to estimate errors and uncertainties in pore-scale and Digital Rock Physics (DRP) problems. The overall predictivity of these studies can be, in fact, hindered by many factors including sample heterogeneity, computational and imaging limitations, model inadequacy and not perfectly known physical parameters. The typical objective of pore-scale studies is the estimation of macroscopic effective parameters such as permeability, effective diffusivity and hydrodynamic dispersion. However, these are often non-deterministic quantities (i.e., results obtained for specific pore-scale sample and setup are not totally reproducible by another “equivalent” sample and setup). The stochastic nature can arise due to the multi-scale heterogeneity, the computational and experimental limitations in considering large samples, and the complexity of the physical models. These approximations, in fact, introduce an error that, being dependent on a large number of complex factors, can be modeled as random. We propose a general simulation tool, based on multilevel Monte Carlo, that can reduce drastically the computational cost needed for computing accurate statistics of effective parameters and other quantities of interest, under any of these random errors. This is, to our knowledge, the first attempt to include Uncertainty Quantification (UQ) in pore-scale physics and simulation. The method can also provide estimates of the discretization error and it is tested on three-dimensional transport problems in heterogeneous materials, where the sampling procedure is done by generation algorithms able to reproduce realistic consolidated and unconsolidated random sphere and ellipsoid packings and arrangements. A totally automatic workflow is developed in an open-source code [2015. https://bitbucket.org/micardi/porescalemc.], that include rigid body physics and random packing algorithms, unstructured mesh discretization, finite volume solvers, extrapolation and post-processing techniques. The proposed method can be efficiently used in many porous media applications for problems such as stochastic homogenization/upscaling, propagation of uncertainty from microscopic fluid and rock properties to macro-scale parameters, robust estimation of Representative Elementary Volume size for arbitrary physics.en
dc.language.isoenen
dc.publisherElsevier BVen
dc.relation.urlhttp://linkinghub.elsevier.com/retrieve/pii/S0309170816300045en
dc.relation.urlhttps://bitbucket.org/micardi/porescalemcen
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Advances in Water Resources. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Advances in Water Resources, 8 February 2016. DOI: 10.1016/j.advwatres.2016.01.004en
dc.subjectPore-scale simulationen
dc.subjectMultilevel Monte Carloen
dc.subjectStochastic upscalingen
dc.subjectUncertainty quantificationen
dc.titleOn the predictivity of pore-scale simulations: estimating uncertainties with multilevel Monte Carloen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalAdvances in Water Resourcesen
dc.eprint.versionPost-printen
dc.contributor.institutionDISAT, Politecnico di Torino, Torino, Italyen
dc.contributor.institutionICES, The University of Texas at Austin, USAen
dc.contributor.institutionMathematics Institute, University of Warwick, UKen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
kaust.authorIcardi, Matteoen
kaust.authorTempone, Raulen
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