Characterization of the Measurement Error in Time-Lapse Seismic Data and Production Data with an EM Algorithm

Zhao, Yu; Li, G.; Reynolds, Albert C.

doi:10.2516/ogst:2007016

Cited by 11 publications

(8 citation statements)

References 21 publications

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“…These noisy observations were provided to the participants but the measurement errors were not provided. In this study, the measurement errors were estimated using the expectation-maximization algorithm developed in [35]. The oil revenue price is $80/STB and both water production and injection costs are $5/STB.…”

Section: Description Of Brugge Fieldmentioning

confidence: 99%

“…If the measurement errors used in EnKF are too small, it can result in loss of variance or even loss of rank in the ensemble covariance which tends to promote ensemble collapse. As TNO did not provide the measurement errors to the participants, we applied the EM algorithm [35] to estimate the measurement errors. Assuming the measurement error is not correlated with time for each type, the estimated variance for producing well BHP, injection well BHP and well rates are, respectively, 48.1 psi 2 , 53.4 psi 2 , and 796.8 (STB/D) 2 .…”

Section: Trial 1: Data Assimilation Without Covariance Localizationmentioning

confidence: 99%

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Closed-loop reservoir management on the Brugge test case

et al. 2010

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This paper proposes an augmented Lagrangian method for production optimization in which the cost function to be maximized is defined as an augmented Lagrangian function consisting of the net present value (NPV) and all the equality and inequality constraints except the bound constraints. The bound constraints are dealt with using a trustregion gradient projection method. The paper also presents a way to eliminate the need to convert the inequality constraints to equality constraints with slack variables in the augmented Lagrangian function, which greatly reduces the size of the optimization problem when the number of inequality constraints is large. The proposed method is tested in the context of closedloop reservoir management benchmark problem based on the Brugge reservoir setup by TNO. In the test, we used the ensemble Kalman filter (EnKF) with covariance localization for data assimilation. Production optimization is done on the updated ensemble mean model from EnKF. The production optimization resulted in a substantial increase in the NPV for the expected reservoir life compared to the base case with reactive control.

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Section: Description Of Brugge Fieldmentioning

confidence: 99%

Section: Trial 1: Data Assimilation Without Covariance Localizationmentioning

confidence: 99%

Closed-loop reservoir management on the Brugge test case

et al. 2010

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“…The EM algorithm in [25] is somewhat similar to that used in [13]. However, EM algorithm can incorporate different types of data and the improved version of the algorithm (spatial EM) incorporates the spatial information among data to enhance the spatial continuity among groups.…”

Section: Introductionmentioning

confidence: 99%

“…Zhao et al [25] applied a spatial EM algorithm to group seismic and production data for the purpose of estimating measurement error. The EM algorithm in [25] is somewhat similar to that used in [13].…”

Section: Introductionmentioning

confidence: 99%

“…When two data points are far away in space, the penalty term prevents them from falling into the same group. In this paper, we apply three different EM algorithms: the standard EM algorithm without any spatial constraint, the neighborhood EM (NEM) algorithm and the spatial EM algorithm developed in [23] and [25] to estimate the distribution of maps of facies from seismic data.…”

Section: Introductionmentioning

confidence: 99%

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Application of EM algorithms for seismic facices classification

Han

Zhao²,

et al. 2010

Comput Geosci

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Identification of the geological facies and their distribution from seismic and other available geological information is important during the early stage of reservoir development (e.g. decision on initial well locations). Traditionally, this is done by manually inspecting the signatures of the seismic attribute maps, which is very time-consuming. This paper proposes an application of the Expectation-Maximization (EM) algorithm to automatically identify geological facies from seismic data. While the properties within a certain geological facies are relatively homogeneous, the properties between geological facies can be rather different. Assuming that noisy seismic data of a geological facies, which reflect rock properties, can be approximated with a Gaussian distribution, the seismic data of a reservoir composed of several geological facies are samples from a Gaussian mixture model. The mean of each Gaussian model represents the average value of the seismic data within each facies while the variance gives the variation of the seismic data within a facies. The proportions in the Gaussian mixture model represent the relative volumes of different facies in the reservoir. In this setting, the facies classification problem becomes a problem of estimating the parameters defining the Gaussian mixture model. The EM algorithm has long been used to estimate Gaussian mixture model parameters. As the standard EM algorithm does not consider spatial relationship among data, it can generate spatially scattered seismic facies which is physically unrealistic. We improve the standard EM algorithm by adding a spatial constraint to enhance spatial continuity of the estimated geological facies. By applying the EM algorithms to acoustic impedance and Poisson's ratio data for two synthetic examples, we are able to identify the facies distribution.

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