Structural Surface Uncertainty Modeling and Updating Using the Ensemble Kalman Filter

Summary Although typically large uncertainties are associated with reservoir structure, the reservoir geometry is usually fixed to a single interpretation in history-matching workflows, and focus is on the estimation of geological properties such as facies location, porosity, and permeability fields. Structural uncertainties can have significant effects on the bulk reservoir volume, well planning, and predictions of future production. In this paper, we consider an integrated reservoir-characterization workflow for structural-uncertainty assessment and continuous updating of the structural reservoir model by assimilation of production data. We address some of the challenges linked to structural-surface updating with the ensemble Kalman filter (EnKF). An ensemble of reservoir models, expressing explicitly the uncertainty resulting from seismic interpretation and time-to-depth conversion, is created. The top and bottom reservoir-horizon uncertainties are considered as a parameter for assisted history matching and are updated by sequential assimilation of production data using the EnKF. To avoid modifications in the grid architecture and thus to ensure a fixed dimension of the state vector, an elastic-grid approach is proposed. The geometry of a base-case simulation grid is deformed to match the realizations of the top and bottom reservoir horizons. The method is applied to a synthetic example, and promising results are obtained. The result is an ensemble of history-matched structural models with reduced and quantified uncertainty. The updated ensemble of structures provides a more reliable characterization of the reservoir architecture and a better estimate of the field oil in place.

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Importance of Distributed Temperature Sensor Data for Steam Assisted Gravity Drainage Reservoir Characterization and History Matching Within Ensemble Kalman Filter Framework

Journal of Energy Resources Technology ◽

10.1115/1.4027763 ◽

2015 ◽

Vol 137 (4) ◽

Cited By ~ 12

Author(s):

Amit Panwar ◽

Japan J. Trivedi ◽

Siavash Nejadi

Keyword(s):

Kalman Filter ◽

Ensemble Kalman Filter ◽

History Matching ◽

Reservoir Characterization ◽

Temperature Data ◽

Gravity Drainage ◽

Production Data ◽

Facies Distribution ◽

Steam Assisted Gravity Drainage ◽

Temperature Observations

Distributed temperature sensing (DTS), an optical fiber down-hole monitoring technique, provides a continuous and permanent well temperature profile. In steam assisted gravity drainage (SAGD) reservoirs, the DTS plays an important role to provide depth-and-time continuous temperature measurement for steam management and production optimization. These temperature observations provide useful information for reservoir characterization and shale detection in SAGD reservoirs. However, use of these massive data for automated SAGD reservoir characterization has not been investigated. The ensemble Kalman filter (EnKF), a parameter estimation approach using these real-time temperature observations, provides a highly attractive algorithm for automatic history matching and quantitative reservoir characterization. Due to its complex geological nature, the shale barrier exhibits as a different facies in sandstone reservoirs. In such reservoirs, due to non-Gaussian distributions, the traditional EnKF underestimates the uncertainty and fails to obtain a good production data match. We implemented discrete cosine transform (DCT) to parameterize the facies labels with EnKF. Furthermore, to capture geologically meaningful and realistic facies distribution in conjunction with matching observed data, we included fiber-optic sensor temperature data. Several case studies with different facies distribution and well configurations were conducted. In order to investigate the effect of temperature observations on SAGD reservoir characterization, the number of DTS observations and their locations were varied for each study. The qualities of the history-matched models were assessed by comparing the facies maps, facies distribution, and the root mean square error (RMSE) of the predicted data mismatch. Use of temperature data in conjunction with production data demonstrated significant improvement in facies detection and reduced uncertainty for SAGD reservoirs. The RMSE of the predicted data is also improved. The results indicate that the assimilation of DTS data from nearby steam chamber location has a significant potential in significant reduction of uncertainty in steam chamber propagation and production forecast.

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A Probabilistic Collocation-Based Kalman Filter for History Matching

SPE Journal ◽

10.2118/140737-pa ◽

2011 ◽

Vol 16 (02) ◽

pp. 294-306 ◽

Cited By ~ 22

Author(s):

Lingzao Zeng ◽

Haibin Chang ◽

Dongxiao Zhang

Keyword(s):

Kalman Filter ◽

Data Assimilation ◽

Ensemble Kalman Filter ◽

History Matching ◽

Initial Conditions ◽

Collocation Point ◽

Computational Effort ◽

Production Data ◽

Sampling Errors ◽

Probabilistic Collocation

Summary The ensemble Kalman filter (EnKF) has been used widely for data assimilation. Because the EnKF is a Monte Carlo-based method, a large ensemble size is required to reduce the sampling errors. In this study, a probabilistic collocation-based Kalman filter (PCKF) is developed to adjust the reservoir parameters to honor the production data. It combines the advantages of the EnKF for dynamic data assimilation and the polynomial chaos expansion (PCE) for efficient uncertainty quantification. In this approach, all the system parameters and states and the production data are approximated by the PCE. The PCE coefficients are solved with the probabilistic collocation method (PCM). Collocation realizations are constructed by choosing collocation point sets in the random space. The simulation for each collocation realization is solved forward in time independently by means of an existing deterministic solver, as in the EnKF method. In the analysis step, the needed covariance is approximated by the PCE coefficients. In this study, a square-root filter is employed to update the PCE coefficients. After the analysis, new collocation realizations are constructed. With the parameter collocation realizations as the inputs and the state collocation realizations as initial conditions, respectively, the simulations are forwarded to the next analysis step. Synthetic 2D water/oil examples are used to demonstrate the applicability of the PCKF in history matching. The results are compared with those from the EnKF on the basis of the same analysis. It is shown that the estimations provided by the PCKF are comparable to those obtained from the EnKF. The biggest improvement of the PCKF comes from the leading PCE approximation, with which the computational burden of the PCKF can be greatly reduced by means of a smaller number of simulation runs, and the PCKF outperforms the EnKF for a similar computational effort. When the correlation ratio is much smaller, the PCKF still provides estimations with a better accuracy for a small computational effort.

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Importance of Distributed Temperature Sensor (DTS) Placement for SAGD Reservoir Characterization and History Matching Within Ensemble Kalman Filter (EnKF) Framework

10.2118/153659-ms ◽

2012 ◽

Cited By ~ 1

Author(s):

Amit Panwar ◽

Japan J. Trivedi ◽

Siavash Nejadi

Keyword(s):

Kalman Filter ◽

Ensemble Kalman Filter ◽

Temperature Sensor ◽

History Matching ◽

Reservoir Characterization ◽

Distributed Temperature Sensor

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History Matching Using the Ensemble Kalman Filter With Multiscale Parameterization: A Field Case Study

SPE Journal ◽

10.2118/118879-pa ◽

2010 ◽

Vol 16 (02) ◽

pp. 307-317 ◽

Cited By ~ 22

Author(s):

Yanfen Zhang ◽

Dean S. Oliver

Keyword(s):

Kalman Filter ◽

Ensemble Kalman Filter ◽

History Matching ◽

Multiple Scales ◽

Gaussian Random Fields ◽

Rock Properties ◽

Real Field ◽

Production Data ◽

Reservoir Properties ◽

Water Cut

Summary The increased use of optimization in reservoir management has placed greater demands on the application of history matching to produce models that not only reproduce the historical production behavior but also preserve geological realism and quantify forecast uncertainty. Geological complexity and limited access to the subsurface typically result in a large uncertainty in reservoir properties and forecasts. However, there is a systematic tendency to underestimate such uncertainty, especially when rock properties are modeled using Gaussian random fields. In this paper, we address one important source of uncertainty: the uncertainty in regional trends by introducing stochastic trend coefficients. The multiscale parameters including trend coefficients and heterogeneities can be estimated using the ensemble Kalman filter (EnKF) for history matching. Multiscale heterogeneities are often important, especially in deepwater reservoirs, but are generally poorly represented in history matching. In this paper, we describe a method for representing and updating multiple scales of heterogeneity in the EnKF. We tested our method for updating these variables using production data from a deepwater field whose reservoir model has more than 200,000 unknown parameters. The match of reservoir simulator forecasts to real field data using a standard application of EnKF had not been entirely satisfactory because it was difficult to match the water cut of a main producer in the reservoir. None of the realizations of the reservoir exhibited water breakthrough using the standard parameterization method. By adding uncertainty in large-scale trends of reservoir properties, the ability to match the water cut and other production data was improved substantially. The results indicate that an improvement in the generation of the initial ensemble and in the variables describing the property fields gives an improved history match with plausible geology. The multiscale parameterization of property fields reduces the tendency to underestimate uncertainty while still providing reservoir models that match data.

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Assessing the Uncertainty in Reservoir Description and Performance Predictions With the Ensemble Kalman Filter

SPE Journal ◽

10.2118/95750-pa ◽

2007 ◽

Vol 12 (03) ◽

pp. 382-391 ◽

Cited By ~ 52

Author(s):

Mohammad Zafari ◽

Albert Coburn Reynolds

Keyword(s):

Kalman Filter ◽

Ensemble Kalman Filter ◽

History Matching ◽

Reservoir Characterization ◽

Reservoir Performance ◽

Reservoir Models ◽

Performance Predictions ◽

And Performance ◽

Reservoir Description

Summary Recently, the ensemble Kalman Filter (EnKF) has gained popularity in atmospheric science for the assimilation of data and the assessment of uncertainty in forecasts for complex, large-scale problems. A handful of papers have discussed reservoir characterization applications of the EnKF, which can easily and quickly be coupled with any reservoir simulator. Neither adjoint code nor specific knowledge of simulator numerics is required for implementation of the EnKF. Moreover, data are assimilated (matched) as they become available; a suite of plausible reservoir models (the ensemble, set of ensemble members or suite or realizations) is continuously updated to honor data without rematching data assimilated previously. Because of these features, the method is far more efficient for history matching dynamic data than automatic history matching based on optimization algorithms. Moreover, the set of realizations provides a way to evaluate the uncertainty in reservoir description and performance predictions. Here we establish a firm theoretical relation between randomized maximum likelihood and the ensemble Kalman filter. Although we have previously generated reservoir characterization examples where the method worked well, here we also provide examples where the performance of EnKF does not provide a reliable characterization of uncertainty. Introduction Our main interest is in characterizing the uncertainty in reservoir description and reservoir performance predictions in order to optimize reservoir management. To do so, we wish to generate a suite of plausible reservoir models (realizations) that are consistent with all information and data. If the set of models is obtained by correctly sampling the pdf, then the set of models give a characterization of the uncertainty in the reservoir model. Thus, by predicting future reservoir performance with each of the realizations, and calculating statistics on the set of outcomes, one can evaluate the uncertainty in reservoir performance predictions.

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