A model-independent iterative ensemble smoother for efficient history-matching and uncertainty quantification in very high dimensions

2018 ◽  
Vol 109 ◽  
pp. 191-201 ◽  
Author(s):  
Jeremy T. White
Keyword(s):  
Uncertainty Quantification ◽  
History Matching ◽  
High Dimensions ◽  
Ensemble Smoother ◽  
Model Independent ◽  
Iterative Ensemble Smoother ◽  
Very High

Improved Estimation and Forecasting Through Residual-Based Model Error Quantification

SPE Journal ◽  
2020 ◽  
Vol 25 (02) ◽  
pp. 951-968 ◽  
Author(s):  
Minjie Lu ◽  
Yan Chen
Keyword(s):  
History Matching ◽  
Historical Data ◽  
Total Error ◽  
Model Error ◽  
Complex Nature ◽  
Model Parameters ◽  
Observation Error ◽  
Model Errors ◽  
Ensemble Smoother ◽  
Iterative Ensemble Smoother

Summary Owing to the complex nature of hydrocarbon reservoirs, the numerical model constructed by geoscientists is always a simplified version of reality: for example, it might lack resolution from discretization and lack accuracy in modeling some physical processes. This flaw in the model that causes mismatch between actual observations and simulated data when “perfect” model parameters are used as model inputs is known as “model error”. Even in a situation when the model is a perfect representation of reality, the inputs to the model are never completely known. During a typical model calibration procedure, only a subset of model inputs is adjusted to improve the agreement between model responses and historical data. The remaining model inputs that are not calibrated and are likely fixed at incorrect values result in model error in a similar manner as the imperfect model scenario. Assimilation of data without accounting for model error can result in the incorrect adjustment to model parameters, the underestimation of prediction uncertainties, and bias in forecasts. In this paper, we investigate the benefit of recognizing and accounting for model error when an iterative ensemble smoother is used to assimilate production data. The correlated “total error” (a combination of model error and observation error) is estimated from the data residual after a standard history-matching using the Levenberg-Marquardt form of iterative ensemble smoother (LM-EnRML). This total error is then used in further data assimilations to improve the estimation of model parameters and quantification of prediction uncertainty. We first illustrate the method using a synthetic 2D five-spot example, where some model errors are deliberately introduced, and the results are closely examined against the known “true” model. Then, the Norne field case is used to further evaluate the method. The Norne model has previously been history-matched using the LM-EnRML (Chen and Oliver 2014), where cell-by-cell properties (permeability, porosity, net-to-gross, vertical transmissibility) and parameters related to fault transmissibility, depths of water/oil contacts, and relative permeability function are adjusted to honor historical data. In this previous study, the authors highlighted the importance of including large amounts of model parameters, the proper use of localization, and heuristic adjustment of data noise to account for modeling error. In this paper, we improve the last aspect by quantitatively estimating model error using residual analysis.

scholarly journals Revising the stochastic iterative ensemble smoother

2019 ◽  
Author(s):  
Patrick N. Raanes ◽  
Andreas S. Stordal ◽  
Geir Evensen
Keyword(s):  
Data Assimilation ◽  
History Matching ◽  
Kalman Smoother ◽  
Multiple Data ◽  
Current Formulation ◽  
Ensemble Smoother ◽  
Careful Treatment ◽  
Randomized Maximum Likelihood ◽  
Iterative Ensemble Smoother ◽  
Lorenz 96

Abstract. Ensemble randomized maximum likelihood (EnRML) is an iterative (stochastic) ensemble smoother, used for large and nonlinear inverse problems, such as history matching and data assimilation. Its current formulation is overly complicated and has issues with computational costs, noise, and covariance localization, even causing some practitioners to omit crucial prior information. This paper resolves these difficulties and streamlines the algorithm, without changing its output. These simplifications are achieved through the careful treatment of the linearizations and subspaces. For example, it is shown (a) how ensemble linearizations relate to average sensitivity, and (b) that the ensemble does not loose rank during updates. The paper also draws significantly on the theory of the (deterministic) iterative ensemble Kalman smoother (IEnKS). Comparative benchmarks are obtained with the Lorenz-96 model with these two smoothers and the ensemble smoother using multiple data assimilation (ES-MDA).

History Matching of the Norne Full-Field Model With an Iterative Ensemble Smoother

2014 ◽  
Vol 17 (02) ◽  
pp. 244-256 ◽  
Author(s):  
Yan Chen ◽  
Dean S. Oliver
Keyword(s):  
History Matching ◽  
Oil And Gas ◽  
Field Model ◽  
Model Parameters ◽  
Data Types ◽  
Full Field ◽  
Ensemble Smoother ◽  
Main Fault ◽  
Iterative Ensemble Smoother ◽  
Partial Communication

Summary Although ensemble-based data-assimilation methods such as the ensemble Kalman filter (EnKF) and the ensemble smoother have been extensively used for the history matching of synthetic models, the number of applications of ensemble-based methods for history matching of field cases is extremely limited. In most of the published field cases in which the ensemble-based methods were used, the number of wells and the types of data to be matched were relatively small. As a result, it may not be clear to practitioners how a real history-matching study would be accomplished with ensemble-based methods. In this paper, we describe the application of the iterative ensemble smoother to the history matching of the Norne field, a North Sea field, with a moderately large number of wells, a variety of data types, and a relatively long production history. Particular attention is focused on the problems of the identification of important variables, the generation of an initial ensemble, the plausibility of results, and the efficiency of minimization. We also discuss the challenges encountered in the use of the ensemble-based method for complex-field case studies that are not typically encountered in synthetic cases. The Norne field produces from an oil-and-gas reservoir discovered in 1991 offshore Norway. The full-field model consists of four main fault blocks that are in partial communication and many internal faults with uncertain connectivity in each fault block. There have been 22 producers and 9 injectors in the field. Water-alternating-gas injection is used as the depletion strategy. Production rates of oil, gas, and water of 22 producers from 1997 to 2006 and repeat-formation-tester (RFT) pressure from 14 different wells are available for model calibration. The full-field simulation model has 22 layers, each with a dimension of 46 × 112 cells. The total number of active cells is approximately 45,000. The Levenberg-Marquardt form of the iterative ensemble smoother (LM-EnRML) is used for history matching. The model parameters that are updated include permeability, porosity, and net-to-gross (ntg) ratio at each gridblock; vertical transmissibility at each gridblock for six layers; transmissibility multipliers of 53 faults; endpoint water and gas relative permeability of four different reservoir zones; depth of water/oil contacts; and transmissibility multipliers between a few main fault blocks. The total number of model parameters is approximately 150,000. Distance-based localization is used to regularize the updates from LM-EnRML. LM-EnRML is able to achieve improved data match compared with the manually history-matched model after three iterations. Updates from LM-EnRML do not introduce artifacts in the property fields as in the manually history-matched model. The automated workflow is also much less labor-intensive than that for manual history matching.

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