Crisman Annual Report 2009 - Harold Vance Department of ...

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Stochastic History Matching, Forecasting, and Production with the Ensemble Kalman Filter Introduction 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, despite the progress that has been made, development of more accurate and efficient history matching techniques that produce geologically realistic outcomes (reservoir models) is still one of the main challenges for reservoir engineers, mainly due to the high complexity of the problem, data scarcity, and computational demand for field applications. Because of the insufficient information about reservoir spatial property distribution, history matching of heterogeneous reservoirs is an inherently ill-posed inverse problem; that is, it is possible to obtain several reservoir models that honor observed measurements but have geologically distinct features and provide incorrect predictions. Two common approaches to deal with ill-posed history matching problems are either to constrain the structural form of acceptable solutions (regularization) or to reduce the number of unknown parameters (reparameterization). While these methods have been successfully used as effective strategies to improve the solution of ill-posed inverse problems, they may not provide accurate solutions where a simple structural assumption can be defined for features with more complex geometry. for incorporating dynamic flow measurements into multipoint pattern simulation with the Single Normal Equation SIMulation (SNESIM) algorithm. Accomplishments The generated probability map represents the main information in the nonlinear dynamic measurements and can be easily integrated into the SNESIM algorithm to simulate an updated ensemble of conditional facies (Fig. 1b). We have illustrated the effectiveness of this approach through several experiments. The results of development have been summarized into a manuscript that is currently being reviewed in the Computational Geosciences Journal. Figure 1 shows a simple example from the manuscript that is undergoing review. Future Work We are currently working to advance the implementation of our approach to deal with uncertainty in the training image that is used for pattern simulation and to address some of the limitations of the EnKF-based implementation of our algorithm. (continued on next page) Objectives The ensemble Kalman filter (EnKF) has recently been introduced to reservoir engineering literature as a promising history matching technique. It is easy to implement, provides considerable flexibility for describing reservoir model uncertainty, and supplies valuable information about reservoir performance prediction uncertainty. Among the limitations of the EnKF is its covariance-based (second order) model updating scheme that restricts its application to estimate discrete geological objects that are not amenable to covariance-based descriptions. When the standard EnKF implementation is used to update facies permeability values in each grid block (Fig. 1a), the connectivity between the existing features is not preserved even when facies description is parameterized to encourage continuity. In this project, by using the EnKF to generate a probability map to describe the spatial distribution of facies, we are developing a more consistent approach Crisman Annual Report 2009 CRISMAN INSTITUTE Project Information 3.6.6 Stochastic History Matching, Forecasting, and Production with the Ensemble Kalman Filter Contacts Behnam Jafarpour 979.845.0666 behnam.jafarpour@pe.tamu.edu Morteza Khodabakhshi 79
(a) Standard EnKF for permeability estimation True Perm. (b) Prob. Map estimation with EnKF initial 3 months 6 months 18 months 36 months initial 3 months 6 months 18 months 36 months ens. mean ens. mean sample 5 prob. map sample 5 sample 4 sample 4 sample 3 sample 3 sample 2 sample 2 sample 1 sample 1 Fig. 1. Facies estimation from production data using the standard EnKF implementation (a), and application of EnKF to update the probability map of facies distribution (b). In (a), the First to Fifth rows show the evolution of sample permeability fields in time (after update steps) with the mean of 300 samples shown in the Sixth row. In (b), the update to the probability map is shown in the First row while the resulting permeability facies from the SNESIM algorithm are shown in the Second to Sixth rows. The last row contains the mean of the 300 sample permeabilities. 80 Crisman Annual Report 2009
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Harold Vance Department of Petroleu
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Issue 3, February 2010 Stephen A. H
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Combustion Assisted Gravity Drainag
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6 Crisman Annual Report 2009
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Summary The Crisman Institute has t
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Membership History The Crisman Inst
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An Advisory System for Selecting Dr
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A procedure to measure the viscosit
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PRISE - Petroleum Resource Investig
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Gas Shales Simulation and Productio
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Characterization of Rock Transport
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An Analytical Approach to Model Sha
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P90 P50 P10 Fig. 3. P10, P50 and P9
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Page 51 and 52: Propagation of Induced Hydraulic Fr
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Page 67 and 68: Evaluation of Polymer-Based In-Situ
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Page 93 and 94: and Catalyst. Paper presented at th
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