Data Assimilation

Data Assimilation
Author: Geir Evensen
Publisher: Springer Science & Business Media
Total Pages: 285
Release: 2006-12-22
Genre: Science
ISBN: 3540383018

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This book reviews popular data-assimilation methods, such as weak and strong constraint variational methods, ensemble filters and smoothers. The author shows how different methods can be derived from a common theoretical basis, as well as how they differ or are related to each other, and which properties characterize them, using several examples. Readers will appreciate the included introductory material and detailed derivations in the text, and a supplemental web site.

An Ensemble Kalman Filter Module for Automatic History Matching

An Ensemble Kalman Filter Module for Automatic History Matching
Author: Baosheng Liang
Publisher:
Total Pages: 0
Release: 2007
Genre: Hydrocarbon reservoirs
ISBN:

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The data assimilation process of adjusting variables in a reservoir simulation model to honor observations of field data is known as history matching and has been extensively studied for few decades. However, limited success has been achieved due to the high complexity of the problem and the large computational effort required by the practical applications. An automatic history matching module based on the ensemble Kalman filter is developed and validated in this dissertation. The ensemble Kalman filter has three steps: initial sampling, forecasting through a reservoir simulator, and assimilation. The initial random sampling is improved by the singular value decomposition, which properly selects the ensemble members with less dependence. In this way, the same level of accuracy is achieved through a smaller ensemble size. Four different schemes for the assimilation step are investigated and direct inverse and square root approaches are recommended. A modified ensemble Kalman filter algorithm, which addresses the preference to the ensemble members through a nonequally weighting factor, is proposed. This weighted ensemble Kalman filter generates better production matches and recovery forecasting than those from the conventional ensemble Kalman filter. The proposed method also has faster convergence at the early time period of history matching. Another variant, the singular evolutive interpolated Kalman filter, is also applied. The resampling step in this method appears to improve the filter stability and help the filter to deliver rapid convergence both in model and data domains. This method and the ensemble Kalman filter are effective for history matching and forecasting uncertainty quantification. The independence of the ensemble members during the forecasting step allows the benefit of high-performance computing for the ensemble Kalman filter implementation during automatic history matching. Two-level computation is adopted; distributing ensemble members simultaneously while simulating each member in a parallel style. Such computation yields a significant speedup. The developed module is integrated with reservoir simulators UTCHEM, GEM and ECLIPSE, and has been implemented in the framework Integrated Reservoir Simulation Platform (IRSP). The successful applications to two and three-dimensional cases using blackoil and compositional reservoir cases demonstrate the efficiency of the developed automatic history matching module.

History-matching of Petroleum Reservoir Models by the Ensemble Kalman Filter and Parameterization Methods

History-matching of Petroleum Reservoir Models by the Ensemble Kalman Filter and Parameterization Methods
Author: Leila Heidari
Publisher:
Total Pages: 224
Release: 2011
Genre:
ISBN:

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History-matching enables integration of data acquired after the production in the reservoir model building workflow. Ensemble Kalman Filter (EnKF) is a sequential assimilation or history-matching method capable of integrating the measured data as soon as they are obtained. This work is based on the EnKF application for History-matching purposes and is divided into two main sections. First section deals with the application of the EnKF to several case studies in order to better understand the merits and shortcomings of the method. These case studies include two synthetic case studies (a simple one and a rather complex one), a Facies model and a real reservoir model. In most cases the method is successful in reproducing the measured data. The encountered problems are explained and possible solutions are proposed. Second section deals with two newly proposed algorithms combining the EnKF with two parameterization methods: pilot point method and gradual deformation method, which are capable of preserving second order statistical properties (mean and covariance). Both developed algorithms are applied to the simple synthetic case study. For the pilot point method, the application was successful through an adequate number and proper positioning of pilot points. In case of the gradual deformation, the application can be successful provided the background ensemble is large enough. For both cases, some improvement scenarios are proposed and further applications to more complex scenarios are recommended.

Inverse Theory for Petroleum Reservoir Characterization and History Matching

Inverse Theory for Petroleum Reservoir Characterization and History Matching
Author: Dean S. Oliver
Publisher: Cambridge University Press
Total Pages: 394
Release: 2008-05-01
Genre: Science
ISBN: 9780521881517

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This book is a guide to the use of inverse theory for estimation and conditional simulation of flow and transport parameters in porous media. It describes the theory and practice of estimating properties of underground petroleum reservoirs from measurements of flow in wells, and it explains how to characterize the uncertainty in such estimates. Early chapters present the reader with the necessary background in inverse theory, probability and spatial statistics. The book demonstrates how to calculate sensitivity coefficients and the linearized relationship between models and production data. It also shows how to develop iterative methods for generating estimates and conditional realizations. The text is written for researchers and graduates in petroleum engineering and groundwater hydrology and can be used as a textbook for advanced courses on inverse theory in petroleum engineering. It includes many worked examples to demonstrate the methodologies and a selection of exercises.

Nonlinear Data Assimilation

Nonlinear Data Assimilation
Author: Peter Jan Van Leeuwen
Publisher: Springer
Total Pages: 130
Release: 2015-07-22
Genre: Mathematics
ISBN: 3319183478

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This book contains two review articles on nonlinear data assimilation that deal with closely related topics but were written and can be read independently. Both contributions focus on so-called particle filters. The first contribution by Jan van Leeuwen focuses on the potential of proposal densities. It discusses the issues with present-day particle filters and explorers new ideas for proposal densities to solve them, converging to particle filters that work well in systems of any dimension, closing the contribution with a high-dimensional example. The second contribution by Cheng and Reich discusses a unified framework for ensemble-transform particle filters. This allows one to bridge successful ensemble Kalman filters with fully nonlinear particle filters, and allows a proper introduction of localization in particle filters, which has been lacking up to now.

Streamline Simulation

Streamline Simulation
Author: Akhil Datta-Gupta
Publisher:
Total Pages: 418
Release: 2007
Genre: Business & Economics
ISBN:

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Streamline-Simulation emphasizes the unique features of streamline technology that in many ways complement conventional finite-difference simulation. It fills gaps in the mathematical foundations.

Handbook of Mathematical Geosciences

Handbook of Mathematical Geosciences
Author: B.S. Daya Sagar
Publisher: Springer
Total Pages: 911
Release: 2018-06-25
Genre: Science
ISBN: 3319789996

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This Open Access handbook published at the IAMG's 50th anniversary, presents a compilation of invited path-breaking research contributions by award-winning geoscientists who have been instrumental in shaping the IAMG. It contains 45 chapters that are categorized broadly into five parts (i) theory, (ii) general applications, (iii) exploration and resource estimation, (iv) reviews, and (v) reminiscences covering related topics like mathematical geosciences, mathematical morphology, geostatistics, fractals and multifractals, spatial statistics, multipoint geostatistics, compositional data analysis, informatics, geocomputation, numerical methods, and chaos theory in the geosciences.

Re-sampling the Ensemble Kalman Filter for Improved History Matching and Characterizations of Non-gaussian and Non-linear Reservoir Models

Re-sampling the Ensemble Kalman Filter for Improved History Matching and Characterizations of Non-gaussian and Non-linear Reservoir Models
Author: Siavash Nejadi
Publisher:
Total Pages: 203
Release: 2014
Genre: Reservoirs
ISBN:

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Reservoir simulation models play an important role in the production forecasting and field development planning. To enhance their predictive capabilities and capture the uncertainties in model parameters, stochastic reservoir models should be calibrated to both geologic and flow observations. The relationship between production performance and model parameters is vastly non-linear, rendering history matching process a challenging task. The Ensemble Kalman Filter (EnKF) is a Monte-Carlo based technique for assisted history matching and real-time updating of reservoir models. EnKF works efficiently with Gaussian variables, but it often fails to honor the reference probability distribution of the model parameters where the distribution of model parameters are non-Gaussian and the system dynamics are strongly nonlinear. In this thesis, novel sampling procedures are proposed to honor geologic information in reservoirs with non-Gaussian model parameters. The methodologies include generating multiple geological models and updating the uncertain parameters using dynamic flow responses using iterative EnKF technique. Two new re-sampling steps are presented for characterization of multiple facies reservoirs. After certain number of assimilation steps, the updated ensemble is used to generate a new ensemble that is conditional to both the geological information and the early production data. Probability field simulation and a novel probability weighted re-sampling scheme are introduce to re-sample a new ensemble. After the re-sampling step, iterative EnKF is again applied on the ensemble members to assimilate the remaining production history. A new automated dynamic data integration workflow is implemented for characterization and uncertainty assessment of fracture reservoir models. This new methodology includes generating multiple discrete fracture network (DFN) models, upscaling the models for flow simulation, and updating the DFN model parameters using dynamic flow responses. The assisted history matching algorithm entails combining a probability weighted sampling with iterative EnKF. The performances of the introduced methodologies are evaluated by performing various simulation studies for different synthetic and field case studies. The qualities of the final matching results are assessed by examining the geological realism of the updated ensemble using the reference probability distribution of the model parameters and computing the predicted dynamic data mismatch.