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

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

doi:10.1029/2010wr009982

Cited by 68 publications

(15 citation statements)

References 93 publications

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“…Note that DCT only applies to tensor product grids and hence has limited practical applications. However, generating basis vectors on unstructured grids is recently developed [49].…”

Section: Parameter Reduction Through Static Compressionmentioning

confidence: 99%

Effective Parametrization for Reliable Reservoir Performance Predictions

Kalla

2012

Int. J. UncertaintyQuantification

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“…Note that DCT only applies to tensor product grids and hence has limited practical applications. However, generating basis vectors on unstructured grids is recently developed [49].…”

Section: Parameter Reduction Through Static Compressionmentioning

confidence: 99%

Effective Parametrization for Reliable Reservoir Performance Predictions

Kalla

2012

Int. J. UncertaintyQuantification

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“…These transforms include the Karhunen-Loève (KL) expansion, which relies on basis functions derived from the prior parameter ensemble, and the discrete cosine transform (DCT), which relies on prespecified basis functions. The DCT used here works especially well for subsurface problems with channelized structures but the KL expansion could also be an attractive option in some problems [32,10]. The DCT can be expressed as:…”

Section: Parameter Reduction With the Discrete Cosine Transformmentioning

confidence: 99%

Efficient Characterization of Uncertain Model Parameters with a Reduced-Order Ensemble Kalman Filter

Lin¹,

McLaughlin²

2014

SIAM J. Sci. Comput.

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Spatially variable model parameters are often highly uncertain and difficult to observe. This has prompted the widespread use of Bayesian characterization methods that can infer parameter values from measurements of related variables, while explicitly accounting for uncertainty. Ensemble versions of Bayesian characterization are particularly convenient when uncertain variables have complex spatial structures that do not conform to Gaussian descriptions. However, ensemble methods can be time consuming for high-dimensional problems. This paper describes a reducedorder approach to ensemble characterization that is particularly well suited for subsurface flow and transport problems. It uses a truncated discrete cosine transform to reduce the dimensionality of spatially variable time-invariant model parameters and a nonlinear extension of principle orthogonal decomposition to reduce the dimensionality of dynamic model states. The resulting nonlinear reduced-order model can be included in the forecast step of a reduced-order ensemble Kalman filter. These concepts are illustrated in a subsurface solute transport problem using ensembles produced by full-and reduced-order models. These ensembles are very similar when there are no measurement updates. When the forecast ensemble is recursively updated with measurements the reduced-order Kalman filter does at least as well as the full-order filter in characterizing a dynamic solute plume, even though its augmented state dimension is only 2% of the dimension of the full-order state. This substantial increase in efficiency implies that a reduced-order filter with the same ensemble size as its full-order counterpart can give comparable performance for orders of magnitude less computational effort or it can use a much larger ensemble for the same computational effort. The possibility of substantial increases in ensemble size could lead to performance improvements through reductions in sampling error and in the rank of the ensemble null space. Also, a reduced-order model similar to the one described here could be used in ensemble real-time control applications, where it can decrease the effort required for both characterization and control.

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“…We apply a hierarchical history matching workflow that consists of two stages (Yin et al, 2011): a global update and a local update. For the global update, the geological model is first parameterized using a Grid Connectivity Transform (GCT) (Bhark et al, 2011). It is a linear transformation where the heterogeneity is updated in a transform domain that is characterized by the spectral modes of the reservoir model grid.…”

Section: Global To Local Hierarchical History Matching Workflowmentioning

confidence: 99%

Streamline-Based Time Lapse Seismic Data Integration Incorporating Pressure and Saturation Effects

Watanabe

Han

Datta‐Gupta

et al. 2013

SPE Annual Technical Conference and Exhibition

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We present an efficient history matching approach that simultaneously integrates 4-D repeat seismic surveys with well production data. This approach is particularly well-suited for the calibration of the reservoir properties of high-resolution geologic models because the seismic data is areally dense but sparse in time, while the production data is continuous in time but averaged over interwell spacing. The joint history matching is performed using streamline-based sensitivities derived from either finite-difference or streamline-based flow simulation. Previous approaches to seismic data integration have mostly incorporated saturation effects but the pressure effects have largely been ignored. We propose, for the first time, streamline-based analytic approaches to compute parameter sensitivities that relate the seismic data to reservoir properties while accounting for both pressure and saturation effects via appropriate rock physics models. The inverted seismic data (e.g., changes in acoustic impedance or fluid saturations), is distributed as a 3-D high-resolution grid cell property or as a vertically integrated two-dimensional map. We derive pressure drop sensitivities along streamlines in addition to our previous work of water saturation sensitivity computation. The novelty of the method lies in the analytic sensitivity computations which make it computationally efficient for high resolution geologic models. We demonstrate the versatility of our approach by implementing it in a finite difference simulator which incorporates detailed physical processes, while the streamline trajectories provide for rapid evaluation of the sensitivities. The efficacy of our proposed approach is demonstrated with both synthetic and field applications. The synthetic example is the SPE benchmark Brugge field case. The field example involves waterflooding of a North Sea reservoir with multiple seismic surveys. For both the synthetic and the field cases, the advantages of incorporating the time-lapse variations are clearly demonstrated through improved estimation of the permeability distribution, pressure profile, and fluid saturation evolution and swept volumes.

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

Cited by 68 publications

References 93 publications

Effective Parametrization for Reliable Reservoir Performance Predictions

Effective Parametrization for Reliable Reservoir Performance Predictions

Efficient Characterization of Uncertain Model Parameters with a Reduced-Order Ensemble Kalman Filter

Streamline-Based Time Lapse Seismic Data Integration Incorporating Pressure and Saturation Effects

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