The effect of error models in the multiscale inversion of binary permeability fields.
Abstract
We present results from a recently developed multiscale inversion technique for binary media, with emphasis on the effect of subgrid model errors on the inversion. Binary media are a useful finescale representation of heterogeneous porous media. Averaged properties of the binary field representations can be used to characterize flow through the porous medium at the macroscale. Both direct measurements of the averaged properties and upscaling are complicated and may not provide accurate results. However, it may be possible to infer upscaled properties of the binary medium from indirect measurements at the coarse scale. Multiscale inversion, performed with a subgrid model to connect disparate scales together, can also yield information on the finescale properties. We model the binary medium using truncated Gaussian fields, and develop a subgrid model for the upscaled permeability based on excursion sets of those fields. The subgrid model requires an estimate of the proportion of inclusions at the block scale as well as some geometrical parameters of the inclusions as inputs, and predicts the effective permeability. The inclusion proportion is assumed to be spatially varying, modeled using Gaussian processes and represented using a truncated KarhunenLouve (KL) expansion. This expansion is used, along with the subgrid model, tomore »
 Authors:

 Massachusetts Institute of Technology, Cambridge, MA
 Sandia National Laboratories, Albuquerque, NM
 Publication Date:
 Research Org.:
 Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1038997
 Report Number(s):
 SAND20108695C
TRN: US201209%%104
 DOE Contract Number:
 AC0494AL85000
 Resource Type:
 Conference
 Resource Relation:
 Conference: Proposed for presentation at the American Geophysical Union Fall Meeting held December 1317, 2010 in San Francisco, CA.
 Country of Publication:
 United States
 Language:
 English
 Subject:
 58 GEOSCIENCES; GAUSSIAN PROCESSES; GEOMETRY; HYDROLOGY; MONTE CARLO METHOD; PERMEABILITY; SIMULATION; TRANSPORT; GEOPHYSICS
Citation Formats
Marzouk, Youssef M, van Bloemen Waanders, Bart Gustaaf, Ray, Jaideep, and McKenna, Sean Andrew. The effect of error models in the multiscale inversion of binary permeability fields.. United States: N. p., 2010.
Web.
Marzouk, Youssef M, van Bloemen Waanders, Bart Gustaaf, Ray, Jaideep, & McKenna, Sean Andrew. The effect of error models in the multiscale inversion of binary permeability fields.. United States.
Marzouk, Youssef M, van Bloemen Waanders, Bart Gustaaf, Ray, Jaideep, and McKenna, Sean Andrew. Wed .
"The effect of error models in the multiscale inversion of binary permeability fields.". United States.
@article{osti_1038997,
title = {The effect of error models in the multiscale inversion of binary permeability fields.},
author = {Marzouk, Youssef M and van Bloemen Waanders, Bart Gustaaf and Ray, Jaideep and McKenna, Sean Andrew},
abstractNote = {We present results from a recently developed multiscale inversion technique for binary media, with emphasis on the effect of subgrid model errors on the inversion. Binary media are a useful finescale representation of heterogeneous porous media. Averaged properties of the binary field representations can be used to characterize flow through the porous medium at the macroscale. Both direct measurements of the averaged properties and upscaling are complicated and may not provide accurate results. However, it may be possible to infer upscaled properties of the binary medium from indirect measurements at the coarse scale. Multiscale inversion, performed with a subgrid model to connect disparate scales together, can also yield information on the finescale properties. We model the binary medium using truncated Gaussian fields, and develop a subgrid model for the upscaled permeability based on excursion sets of those fields. The subgrid model requires an estimate of the proportion of inclusions at the block scale as well as some geometrical parameters of the inclusions as inputs, and predicts the effective permeability. The inclusion proportion is assumed to be spatially varying, modeled using Gaussian processes and represented using a truncated KarhunenLouve (KL) expansion. This expansion is used, along with the subgrid model, to pose as a Bayesian inverse problem for the KL weights and the geometrical parameters of the inclusions. The model error is represented in two different ways: (1) as a homoscedastic error and (2) as a heteroscedastic error, dependent on inclusion proportionality and geometry. The error models impact the form of the likelihood function in the expression for the posterior density of the objects of inference. The problem is solved using an adaptive Markov Chain Monte Carlo method, and joint posterior distributions are developed for the KL weights and inclusion geometry. Effective permeabilities and tracer breakthrough times at a few 'sensor' locations (obtained by simulating a pump test) form the observables used in the inversion. The inferred quantities can be used to generate an ensemble of permeability fields, both upscaled and finescale, which are consistent with the observations. We compare the inferences developed using the two error models, in terms of the KL weights and finescale realizations that could be supported by the coarsescale inferences. Permeability differences are observed mainly in regions where the inclusions proportion is near the percolation threshold, and the subgrid model incurs its largest approximation. These differences also reflected in the tracer breakthrough times and the geometry of flow streamlines, as obtained from a permeameter simulation. The uncertainty due to subgrid model error is also compared to the uncertainty in the inversion due to incomplete data.},
doi = {},
url = {https://www.osti.gov/biblio/1038997},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2010},
month = {12}
}