Bridging multipoint statistics and truncated Gaussian fields for improved estimation of channelized reservoirs with ensemble methods

Sebacher, Bogdan; Stordal, Andreas S.; Hanea, R.G.

doi:10.1007/s10596-014-9466-3

Cited by 29 publications

(19 citation statements)

References 23 publications

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“…The parameter field is then back transformed to probabilities to create dummy wells and facies realizations are regenerated using the updated information. This is mimicking the resampling step as described in [24] and [23]. This process continuous until a satisfactory data mismatch and geologically plausible realiza-tions are obtained, or until the maximum number of iterations have been reached.…”

Section: Methods and Theorymentioning

confidence: 99%

“…Following [23], given an ensemble of N e facies realizations, for each grid cell C j , estimate the probability of facies type F i (i ϭ 1, 2) as (1) where corresponds to the j th grid cell number in the k th ensemble member. A truncated (marginal) Gaussian parameterization, ⌰, is initiated by defining, for each grid cell C j , a truncation value ␤ j .…”

Section: Facies Parameterizationmentioning

confidence: 99%

“…This procedure can be repeated (in theory infinitely many times) using a re-weighting scheme with possible resampling [24], however, due to the geological constraints we follow [23] and use the updated marginal probability field to regenerate geological realizations.…”

Section: Iterative Adaptive Gaussian Mixture Filter (Iagm)mentioning

confidence: 99%

“…Some parameterization methods are available, such as level-set methods [18], kernel principal component analysis (PCA) [21], Fourier discrete cosine transform (DCT) [17], truncated pluri-Gaussian methods (TPG) [10], etc. The facies parameterization method used here is a normal score parameterization [23] which combines ideas from MPS and TPG. We extend the work of [23] in two directions.…”

Section: Introductionmentioning

confidence: 99%

“…The facies parameterization method used here is a normal score parameterization [23] which combines ideas from MPS and TPG. We extend the work of [23] in two directions. First, instead of using the software specified in [2,27], we use a different commercial software package [22] for facies modeling.…”

Section: Introductionmentioning

confidence: 99%

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Facies Parameterization and Estimation for Complex Reservoirs - The Brugge Field

2015

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Data assimilation using ensemble-based inversion methods has been successfully applied for parameter estimation in reservoir models. However, in certain complex reservoir models, it remains challenging to estimate the model parameters and preserve the geological realism simultaneously. In particular, when handling special reservoir model parameters such as facies types concerning fluvial channels, geological realism becomes one of the key concerns. The main objective of this work is to address this issue on a real field with a newly extended version of a recently proposed facies parameterization approach coupled with ensemble-based data assimilation techniques. The proposed workflow combines the new facies parameterization and the IAGM filter into the data assimilation framework for channelized reservoirs. In order to handle discrete facies parameters, we combine probability maps and truncated Gaussian fields to obtain a continuous parameterization of the facies fields. For the data assimilation we use the Iterative Adaptive Gaussian Mixture (IAGM) Filter, which is an efficient history matching approach that incorporates a resampling routine which allows us to regenerate facies fields using information from the updated probability maps. This workflow is evaluated, for the first time, on a complex field case -the Brugge field. This reservoir model consist of layers with complex channelized structures and layers characterized by reservoir properties generated with variograms. With limited prior knowledge on uncertain facies models, this workflow is shown to be able to preserve the channel continuity while reducing the reservoir model uncertainty with IAGM. When applied to complex real field studies, it provides a geologically consistent and realistic reservoir model which leads to improved capability of predicting subsurface flow behaviors.

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Section: Methods and Theorymentioning

confidence: 99%

Section: Facies Parameterizationmentioning

confidence: 99%

Section: Iterative Adaptive Gaussian Mixture Filter (Iagm)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Facies Parameterization and Estimation for Complex Reservoirs - The Brugge Field

2015

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Discrete Regularization for Calibration of Geologic Facies Against Dynamic Flow Data

Khaninezhad

Golmohammadi

Jafarpour

2018

Water Resources Research

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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.

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Reservoir history matching using constrained ensemble Kalman filtering

et al. 2017

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The high heterogeneity of petroleum reservoirs, represented by their spatially varying rock properties (porosity and permeability), greatly dictates the quantity of recoverable oil. In this work, the estimation of the spatial permeability distribution, which is crucial for predicting the future performance of a reservoir, is carried out through a history matching technique based on constrained ensemble Kalman filtering (EnKF). The main contribution in this work is the novel implementation of hard and soft constraints in the recursive EnKF estimation methodology for petroleum reservoirs. Hard data is obtained from the actual values of the reservoir parameters at discrete locations obtained by core sampling and well logging, while the soft data considered is obtained from correlograms, which characterize the spatial correlation of the rock properties in a reservoir. In each time update, the parameter estimates obtained from the unconstrained EnKF are modified by one of two novel algorithms. In the first, the correlation matrix obtained after the unconstrained EnKF update is transformed to honour the true correlation structure from the correlogram by applying a projection-based method. The second algorithm involves the use of a technique for soft constrained covariance localization. We observe that the soft data constrained localization method results in the best estimates of the permeability and also reduces the computational time significantly. We quantify the improvement in estimation performance of each of the constrained methods over unconstrained estimation. The method, while developed for estimation in petroleum reservoirs, is also generally applicable to systems with spatial heterogeneity and underlying spatial correlations.

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Bridging multipoint statistics and truncated Gaussian fields for improved estimation of channelized reservoirs with ensemble methods

Cited by 29 publications

References 23 publications

Facies Parameterization and Estimation for Complex Reservoirs - The Brugge Field

Facies Parameterization and Estimation for Complex Reservoirs - The Brugge Field

Discrete Regularization for Calibration of Geologic Facies Against Dynamic Flow Data

Reservoir history matching using constrained ensemble Kalman filtering

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