A multiscale method for distributed parameter estimation with application to reservoir history matching

Aanonsen, Sigurd Ivar; Eydinov, Dmitry

doi:10.1007/s10596-005-9012-4

Cited by 23 publications

(25 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These techniques generally involve solving the inverse problem at different levels of discretizations , (i.e., on a multilevel mesh), with conditioning relations (i.e., upscaling and downscaling functions) to link scales together [13,14]. Multiscale solutions primarily differ in the complexity of the conditioning relations and whether the multiscale inference requires iteration between scales.…”

Section: Estimation Of Random Fieldsmentioning

confidence: 99%

Bayesian reconstruction of binary media with unresolved fine-scale spatial structures

Ray

McKenna

Waanders

et al. 2012

Advances in Water Resources

View full text Add to dashboard Cite

We present a Bayesian technique to estimate the fine-scale properties of a binary medium from multiscale observations. The binary medium of interest consists of spatially varying proportions of low and high permeability material with an isotropic structure. Inclusions of one material within the other are far smaller than the domain sizes of interest, and thus are never explicitly resolved. We consider the problem of estimating the spatial distribution of the inclusion proportion, F(x), and a characteristic length-scale of the inclusions, δ, from sparse multiscale measurements. The observations consist of coarse-scale (of the order of the domain size) measurements of the effective permeability of the medium (i.e., static data) and tracer breakthrough times (i.e., dynamic data), which interrogate the fine scale, at a sparsely distributed set of locations. This ill-posed problem is regularized by specifying a Gaussian process model for the unknown field F(x) and expressing it as a superposition of KarhunenLoève modes. The effect of the fine-scale structures on the coarse-scale effective permeability i.e., upscaling, is performed using a subgrid-model which includes δ as one of its parameters. A statistical inverse problem is posed to infer the weights of the Karhunen-Loève modes and δ, which is then solved using an adaptive Markov Chain Monte Carlo method. The solution yields non-parametric distributions for the objects of interest, thus providing most probable estimates and uncertainty bounds on latent structures at coarse and fine scales. The technique is tested using synthetic data. The individual contributions of the static and dynamic data to the inference are also analyzed.

show abstract

Section: Estimation Of Random Fieldsmentioning

confidence: 99%

Bayesian reconstruction of binary media with unresolved fine-scale spatial structures

Ray

McKenna

Waanders

et al. 2012

Advances in Water Resources

View full text Add to dashboard Cite

show abstract

“…These techniques generally involve solving the inverse problem at different levels of discretizations , (i.e., on a multilevel mesh), with conditioning relations (i.e., upscaling and downscaling functions) to link scales together [72,73]. Multiscale solutions primarily differ in the complexity of the conditioning relations and whether the multiscale inference requires iteration between scales.…”

Section: Estimation Of Random Fieldsmentioning

confidence: 99%

Bayesian data assimilation for stochastic multiscale models of transport in porous media.

Marzouk

Waanders

Parno

et al. 2011

View full text Add to dashboard Cite

We investigate Bayesian techniques that can be used to reconstruct field variables from partial observations. In particular, we target fields that exhibit spatial structures with a large spectrum of lengthscales. Contemporary methods typically describe the field on a grid and estimate structures which can be resolved by it. In contrast, we address the reconstruction of grid-resolved structures as well as estimation of statistical summaries of subgrid structures, which are smaller than the grid resolution. We perform this in two different ways (a) via a physical (phenomenological), parameterized subgrid model that summarizes the impact of the unresolved scales at the coarse level and (b) via multiscale finite elements, where specially designed prolongation and restriction operators establish the interscale link between the same problem defined on a coarse and fine mesh. The estimation problem is posed as a Bayesian inverse problem. Dimensionality reduction is performed by projecting the field to be inferred on a suitable orthogonal basis set, viz. the Karhunen-Loève expansion of a multiGaussian. We first demonstrate our techniques on the reconstruction of a binary medium consisting of a matrix with embedded inclusions, which are too small to be grid-resolved. The reconstruction is performed using an adaptive Markov chain Monte Carlo method. We find that the posterior distributions of the inferred parameters are approximately Gaussian. We exploit this finding to reconstruct a permeability field with long, but narrow embedded fractures (which are too fine to be grid-resolved) using scalable ensemble Kalman filters; this also allows us to address larger grids. Ensemble Kalman filtering is then used to estimate the values of hydraulic conductivity and specific yield in a model of the High Plains Aquifer in Kansas. Strong conditioning of the spatial structure of the parameters and the non-linear aspects of the water table aquifer create difficulty for the ensemble Kalman filter. We conclude with a demonstration of the use of multiscale stochastic finite elements to reconstruct permeability fields. This method, though computationally intensive, is general and can be used for multiscale inference in cases where a subgrid model cannot be constructed.

show abstract

“…There is a demand for combining this type of estimate with geostatistical information. In the literature there have been proposed different approaches for including geostatistical information in the optimisation process related to this problem, see, for example, [25][26][27][28]. It could be interesting to combine these types of methodologies with the presented method.…”

Section: Remarks and Future Workmentioning

confidence: 99%

Reservoir description using dynamic parameterisation selection with a combined stochastic and gradient search

Nielsen

Subbey

Christie³

et al. 2006

Comput Geosci

View full text Add to dashboard Cite

There is a correspondence between flow in a reservoir and large scale permeability trends. This correspondence can be derived by constraining reservoir models using observed production data. One of the challenges in deriving the permeability distribution of a field using production data involves determination of the scale of resolution of the permeability. The Adaptive Multiscale Estimation (AME) seeks to overcome the problems related to choosing the resolution of the permeability field by a dynamic parameterisation selection. The standard AME uses a gradient algorithm in solving several optimisation problems with increasing permeability resolution. This paper presents a hybrid algorithm which combines a gradient search and a stochastic algorithm to improve the robustness of the dynamic parameterisation selection. At low dimension, we use the stochastic algorithm to generate several optimised models. We use information from all these produced models to find new optimal refinements, and start out new optimisations with several unequally suggested parameterisations. At higher dimensions we change to a gradient-type optimiser, where the initial solution is chosen from the ensemble of models suggested by the stochastic algorithm. The selection is based on a predefined criterion. We demonstrate the robustness of the hybrid algorithm on sample synthetic cases, which most of them were considered insolvable using the standard AME algorithm.

show abstract

A multiscale method for distributed parameter estimation with application to reservoir history matching

Cited by 23 publications

References 18 publications

Bayesian reconstruction of binary media with unresolved fine-scale spatial structures

Bayesian reconstruction of binary media with unresolved fine-scale spatial structures

Bayesian data assimilation for stochastic multiscale models of transport in porous media.

Reservoir description using dynamic parameterisation selection with a combined stochastic and gradient search

Contact Info

Product

Resources

About