Sparse geologic dictionaries for subsurface flow model calibration: Part II. Robustness to uncertainty

Khaninezhad, Mohammadreza M.; Jafarpour, Behnam; Li, Lianlin

doi:10.1016/j.advwatres.2011.10.005

Cited by 43 publications

(13 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Appendix A: k-SVD Dictionary Learning Khaninezhad et al (2012aKhaninezhad et al ( , 2012b introduced the k-SVD sparse parameterization method for subsurface model calibration and discussed its important properties in comparison with the traditional SVD-based parameterization method. To make the content of the main text accessible without reading the original paper, in this Appendix, we briefly review this algorithm.…”

Section: Discussionmentioning

confidence: 99%

“…The application of the resulting k-SVD dictionary to model calibration is discussed in great detail in Khaninezhad et al (2012aKhaninezhad et al ( , 2012b. When the k-SVD dictionary is used to parameterize the spatial distribution or rock hydraulic properties, i.e., u5Uv, the resulting coefficients v become sparse.…”

Section: Discussionmentioning

confidence: 99%

“…Thus, the solution subspace is not predetermined and has to be found during model calibration. Sparse reconstruction algorithms have been developed to search a relatively large number of the

k

‐SVD expansion functions to identify a subspace (i.e., small subset of expansion functions) that best represents the solution (Khaninezhad et al, ). Sparse reconstruction algorithms use sparsity‐promoting regularization forms that have selection property to identify the best combination of expansion functions based on observed response data (Golmohammadi et al, ; Golmohammadi & Jafarpour, ; Khaninezhad & Jafarpour, ).…”

Section: Methodsmentioning

confidence: 99%

“…In this paper, we primarily focus on the discrete regularization technique. Additional details about the above parameterization methods can be found in Khaninezhad et al (2012aKhaninezhad et al ( , 2012b.…”

Section: Example 1: Tomographic Inversionmentioning

confidence: 99%

See 3 more Smart Citations

Discrete Regularization for Calibration of Geologic Facies Against Dynamic Flow Data

Khaninezhad

Golmohammadi

Jafarpour

2018

Water Resources Research

Self Cite

View full text Add to dashboard Cite

Subsurface flow model calibration involves many more unknowns than measurements, leading to ill‐posed problems with nonunique solutions. To alleviate nonuniqueness, the problem is regularized by constraining the solution space using prior knowledge. In certain sedimentary environments, such as fluvial systems, the contrast in hydraulic properties of different facies types tends to dominate the flow and transport behavior, making the effect of within facies heterogeneity less significant. Hence, flow model calibration in those formations reduces to delineating the spatial structure and connectivity of different lithofacies types and their boundaries. A major difficulty in calibrating such models is honoring the discrete, or piecewise constant, nature of facies distribution. The problem becomes more challenging when complex spatial connectivity patterns with higher‐order statistics are involved. This paper introduces a novel formulation for calibration of complex geologic facies by imposing appropriate constraints to recover plausible solutions that honor the spatial connectivity and discreteness of facies models. To incorporate prior connectivity patterns, plausible geologic features are learned from available training models. This is achieved by learning spatial patterns from training data, e.g., k‐SVD sparse learning or the traditional Principal Component Analysis. Discrete regularization is introduced as a penalty functions to impose solution discreteness while minimizing the mismatch between observed and predicted data. An efficient gradient‐based alternating directions algorithm is combined with variable splitting to minimize the resulting regularized nonlinear least squares objective function. Numerical results show that imposing learned facies connectivity and discreteness as regularization functions leads to geologically consistent solutions that improve facies calibration quality.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

“…Thus, the solution subspace is not predetermined and has to be found during model calibration. Sparse reconstruction algorithms have been developed to search a relatively large number of the

k

Section: Methodsmentioning

confidence: 99%

Section: Example 1: Tomographic Inversionmentioning

confidence: 99%

See 2 more Smart Citations

Discrete Regularization for Calibration of Geologic Facies Against Dynamic Flow Data

Khaninezhad

Golmohammadi

Jafarpour

2018

Water Resources Research

Self Cite

View full text Add to dashboard Cite

show abstract

“…Iterative schemes were also proposed in [3,17,23] in which sparse geologic dictionaries were learned by training over a large set of geological structures, varying in shapes, numbers, and locations. These can potentially lead to enhanced recovery of complex geological structures.…”

Section: The Ensemble Kalman Filter (Enkf) Is a Widely Used Bayesian mentioning

confidence: 99%

A Sparse Bayesian Imaging Technique for Efficient Recovery of Reservoir Channels With Time-Lapse Seismic Measurements

Sana

Ravanelli

Al-Naffouri

et al. 2016

IEEE J. Sel. Top. Appl. Earth Observations Remote Sensing

View full text Add to dashboard Cite

A distance transform for continuous parameterization of discrete geologic facies for subsurface flow model calibration

Hakim-Elahi

Jafarpour

2017

Water Resources Research

Self Cite

View full text Add to dashboard Cite

Construction of predictive subsurface flow models involves subjective interpretation and interpolation of spatially limited data, often using imperfect modeling assumptions. Hence, the process can introduce significant uncertainty and bias in predicting the flow and transport behavior of these systems. In particular, the uncertainty in the facies distribution in complex geologic environments, such as alluvial/fluvial channels, can be consequential for forecasting the dynamic response of these systems to perturbations due to pumping and development activities. Conventional model calibration techniques that are designed to update continuous model parameters cannot be used to estimate discrete parameters from flow and pressure data. We present a distance transform approach for converting discrete facies models to continuous parameters that can be updated using continuous model calibration methods. Distance transforms are widely used in discrete image processing, where the discrete values in each pixel are replaced with their distance (i.e., a continuous variable) to the nearest boundary cell. After updating the continuous distance maps during model calibration, a back transformation is applied to retrieve the updated facies maps. To preserve large‐scale facies connectivity, truncated singular value decomposition (SVD) parametrization may be used to represent the distance maps with low‐rank parameters. A variant of the ensemble smoother, ES‐MDA is used to update the continuous parameters of the inversion (either distance maps or their SVD coefficients if used). The distance transform method addresses an important problem in facies model calibration where model updating can result in losing facies connectivity and discreteness.

show abstract

Sparse geologic dictionaries for subsurface flow model calibration: Part II. Robustness to uncertainty

Cited by 43 publications

References 29 publications

Discrete Regularization for Calibration of Geologic Facies Against Dynamic Flow Data

Discrete Regularization for Calibration of Geologic Facies Against Dynamic Flow Data

A Sparse Bayesian Imaging Technique for Efficient Recovery of Reservoir Channels With Time-Lapse Seismic Measurements

A distance transform for continuous parameterization of discrete geologic facies for subsurface flow model calibration

Contact Info

Product

Resources

About