An adaptively scaled frequency-domain parameterization for history matching

Bhark, Eric; Jafarpour, Behnam; Datta‐Gupta, Akhil

doi:10.1016/j.petrol.2010.11.026

Cited by 15 publications

(9 citation statements)

References 23 publications

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“…In the multiscale algorithm we update the multiplier u from a low modal frequency or coarse spatial description to a higher‐frequency description. We follow the approach to sequential estimation in the frequency domain presented by Bhark et al [2011b] in which similar approaches to data‐driven multiscale calibration algorithms that, as a rule, rescale the geologic model in the spatial domain via sequential refinement or coarsening are also reviewed. The approach of sequential refinement is particularly well suited to our current implementation for two reasons in addition to those emphasized in the literature and is appropriate regardless of prior model information and assumptions.…”

Section: Methodsmentioning

confidence: 99%

“…First, it is geologically consistent to identify or update large‐ before small‐scale structures (e.g., the type of depositional environment may influence smaller length scales and directions of spatial variability), with the latter becoming insensitive to production data beyond some spatial scale [ Vasco et al , 1997; Lu and Horne , 2000; Sahni and Horne , 2005; Bhark et al , 2011b]. In our implementation the sequential refinement of the multiplier field does not update the prior model until a level of detail is reached, if any, at which the multipliers become sensitive to the data.…”

Section: Methodsmentioning

confidence: 99%

“…We consider a second category of linear transform bases that are model independent (or generic) and therefore rely on a general ability to efficiently capture and decorrelate the information of any function in a low‐rank approximation. Two such approaches that have recently been applied in subsurface heterogeneity parameterization are the discrete cosine transform (DCT) basis [ Jafarpour and McLaughlin , 2009; Bhark et al , 2011b] and the discrete wavelet transform (DWT) basis [ Lu and Horne , 2000; Guan et al , 2004; Sahni and Horne , 2005; Jafarpour , 2011], both of which are widely used in image compression [ Gonzales and Woods , 2002]. The DCT, of which there are eight formulations that vary on the basis of the assumption of symmetry at domain boundaries, is a type of Fourier transform that reconstructs a discrete n ‐length signal as the sum of n cosine harmonics [ Britanak et al , 2007].…”

Section: Introductionmentioning

confidence: 99%

“…For the DCT, maximal compression power results from its asymptotic convergence to PCA of a first‐order stationary Markov process [ Ahmed et al , 1974]. Approaches to production data assimilation using the DCT also recognize a key strength as the ability to capture larger scales of geologic continuity and hydraulic property connectivity in the presence of sparse data with a significantly reduced number of parameters [ Jafarpour and McLaughlin , 2009; Bhark et al , 2011b]. That is, a linear combination of lower‐frequency cosine functions naturally enforces field connectivity structure when warranted.…”

Section: Introductionmentioning

confidence: 99%

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A generalized grid connectivity–based parameterization for subsurface flow model calibration

Bhark

Jafarpour

Datta‐Gupta

2011

Water Resources Research

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[1] We develop a novel method of parameterization for spatial hydraulic property characterization to mitigate the challenges associated with the nonlinear inverse problem of subsurface flow model calibration. The parameterization is performed by the projection of the estimable hydraulic property field onto an orthonormal basis derived from the grid connectivity structure. The basis functions represent the modal shapes or harmonics of the grid, are defined by a modal frequency, and converge to special cases of the discrete Fourier series under certain grid geometries and boundary assumptions; therefore, hydraulic property updates are performed in the spectral domain and merge with Fourier analysis in ideal cases. Dependence on the grid alone implies that the basis may characterize any grid geometry, including corner point and unstructured, is model independent, and is constructed off-line and only once prior to flow data assimilation. We apply the parameterization in an adaptive multiscale model calibration workflow for three subsurface flow models. Several different grid geometries are considered. In each case the prior hydraulic property model is updated using a parameterized multiplier field that is superimposed onto the grid and assigned an initial value of unity at each cell. The special case corresponding to a constant multiplier is always applied through the constant basis function. Higher modes are adaptively employed during minimization of data misfit to resolve multiscale heterogeneity in the geomodel. The parameterization demonstrates selective updating of heterogeneity at locations and spatial scales sensitive to the available data, otherwise leaving the prior model unchanged as desired.Citation: Bhark, E. W., B. Jafarpour, and A. Datta-Gupta (2011), A generalized grid connectivity-based parameterization for subsurface flow model calibration, Water Resour. Res., 47, W06517,

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A generalized grid connectivity–based parameterization for subsurface flow model calibration

Bhark

Jafarpour

Datta‐Gupta

2011

Water Resources Research

Self Cite

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“…This was shown to reduce the computational efficiency slightly but greatly simplify the implementation. Bhark et al [61] used gradient-based optimization within a framework of adaptively scaled frequency-domain parameterization. This method reduces the number of parameters through cosine parameterization and uses gradient-based minimization on the data misfit.…”

Section: History Matching For Waterflood and Enhanced Oil Recoverymentioning

confidence: 99%

Review of Field Development Optimization of Waterflooding, EOR, and Well Placement Focusing on History Matching and Optimization Algorithms

et al. 2017

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This paper presents a review of history matching and oil field development optimization techniques with a focus on optimization algorithms. History matching algorithms are reviewed as a precursor to production optimization algorithms. Techniques for history matching and production optimization are reviewed including global and local methods. Well placement, well control, and combined well placement-control optimization using both secondary and tertiary oil production techniques are considered. Secondary and tertiary recovery techniques are commonly referred to as waterflooding and enhanced oil recovery (EOR), respectively. Benchmark models for comparison of methods are summarized while other applications of methods are discussed throughout. No single optimization method is found to be universally superior. Key areas of future work are combining optimization methods and integrating multiple optimization processes. Current challenges and future research opportunities for improved model validation and large scale optimization algorithms are also discussed.

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Ensemble-based multi-scale history-matching using second-generation wavelet transform

et al. 2015

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International audienceEnsemble-based optimization methods are often efficiently applied to history-matching problems. Although satisfactory matches can be obtained, the updated realizations, affected by spurious correlations, generally fail to preserve prior information when using a small ensemble, even when localization is applied. In this work, we propose a multi-scale approach based on grid-adaptive second-generation wavelets. These wavelets can be applied on irregular reservoir grids of any dimensions containing dead or flat cells. The proposed method starts by modifying a few low frequency parameters (coarse scales) and then progressively allows more important updates on a limited number of sensitive parameters of higher resolution (fine scales). The Levenberg-Marquardt ensemble randomized maximum likelihood (LM-enRML) is used as optimization method with a new space-frequency distance-based localization of the Kalman gain, specifically designed for the multi-scale scheme. The algorithm is evaluated on two test cases. The first test is a 2D synthetic case in which several inversions are run using independent ensembles. The second test is the Brugge benchmark case with 10 years of history. The efficiency and quality of results of the multi-scale approach are compared with the grid-block-based LM-enRML with distance-based localization. We observe that the final realizations better preserve the spatial contrasts of the prior models and are less noisy than the realizations updated using a standard grid-block method, while matching the production data equally well

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An adaptively scaled frequency-domain parameterization for history matching

Cited by 15 publications

References 23 publications

A generalized grid connectivity–based parameterization for subsurface flow model calibration

A generalized grid connectivity–based parameterization for subsurface flow model calibration

Review of Field Development Optimization of Waterflooding, EOR, and Well Placement Focusing on History Matching and Optimization Algorithms

Ensemble-based multi-scale history-matching using second-generation wavelet transform

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