Closed Loop Reservoir Management Using the Ensemble Kalman Filter and Sequential Quadratic Programming

2009 ◽  
Author(s):  
Rolf Johan Lorentzen ◽  
Ali Shafieirad ◽  
Geir Naevdal
Keyword(s):  
Kalman Filter ◽  
Quadratic Programming ◽  
Ensemble Kalman Filter ◽  
Sequential Quadratic Programming ◽  
Closed Loop ◽  
Reservoir Management

Some Practical Issues on Real-Time Reservoir Model Updating Using Ensemble Kalman Filter

SPE Journal ◽  
2007 ◽  
Vol 12 (02) ◽  
pp. 156-166 ◽  
Author(s):  
Xian-Huan Wen ◽  
Wen H. Chen
Keyword(s):  
Real Time ◽  
Ensemble Kalman Filter ◽  
Closed Loop ◽  
Model Updating ◽  
Reservoir Management ◽  
Time Interval ◽  
Ensemble Size ◽  
Reservoir Model ◽  
Reservoir Models ◽  
The Impact

Summary The concept of "closed-loop" reservoir management is currently receiving considerable attention in the petroleum industry. A "real-time" or "continuous" reservoir model updating technique is a critical component for the feasible application of any closed-loop, model-based reservoir management process. This technique should be able to rapidly and continuously update reservoir models assimilating the up-to-date observations of production data so that the performance predictions and the associated uncertainty are up-to-date for optimization of future development/operations. The ensemble Kalman filter (EnKF) method has been shown to be quite efficient for this purpose in large-scale nonlinear systems. Previous studies show that a relatively large ensemble size is required for EnKF to reliably assess the uncertainty, and a confirming step is recommended to ensure the consistency of the updated static and dynamic variables with the flow equations. In this paper, we further explore the capability of EnKF, focusing on some practical issues including the correction of the linear and Gaussian assumptions during filter updating with iteration, the reduction of ensemble size with a resampling scheme, and the impact of data assimilation time interval. Results from the example in this paper demonstrate that the proposed iterative EnKF performs better with more accurate predictions and less uncertainty than the traditional noniterative EnKF. The use of iteration reduces the impact of nonlinearity and non-Gaussianity. Results also show that iteration may only be required when predictions are considerably deviated from the observations. The proposed resampling scheme can significantly reduce the ensemble size necessary for reliable assessment of uncertainty with improved accuracy. Finally, we show that the noniterative EnKF is sensitive to the size of time interval between the assimilation steps. Using the proposed iterative EnKF, results are more stable, more accurate reservoir models and predictions can be obtained even when a large time interval is used. This also indicates that iteration within the EnKF updating serves as a process that corrects the stronger nonlinear and non-Gaussian behaviors when larger time interval is used. Introduction Reservoir models have become an important part of day-to-day decision analysis related to management of oil/gas fields. The closed-loop reservoir management concept (Jansen et al. 2005) allows real-time decisions to be made that maximize the production potential of a reservoir. These decisions are based on the most current information available about the reservoir model and the associated uncertainty of the information. One critical requirement in this real-time, model-based reservoir management process is the ability to rapidly estimate the reservoir models and the associated uncertainty reflecting the most current production data in a real-time fashion. Based on a number of studies, the EnKF method was shown to be well-suited for such applications compared to the traditional history-matching (HM) methods (Evensen 1999; Gu and Oliver 2006; Wen and Chen 2006).

Training a convolutional neural network to conserve mass in data assimilation

2021 ◽  
Author(s):  
Yvonne Ruckstuhl ◽  
Tijana Janjic ◽  
Stephan Rasp
Keyword(s):  
Neural Network ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Quadratic Programming ◽  
Convolutional Neural Network ◽  
Ensemble Kalman Filter ◽  
High Dimensional ◽  
Forecast Errors ◽  
The Difference ◽  
Prediction Systems

<p>In previous work, it was shown that preservation of physical properties  in the data assimilation framework can significantly reduce forecast errors. Proposed data assimilation methods, such as the quadratic programming ensemble (QPEns) that can impose such constraints on the calculation of the analysis, are computationally more expensive, severely limiting their application to high dimensional prediction systems as found in earth sciences. We therefore propose to use a convolutional neural network (CNN) trained on the difference between the analysis produced by a standard ensemble Kalman Filter (EnKF) and the QPEns to correct any violations of imposed constraints. On this poster, we focus on conservation of mass and show in an idealized setup that the hybrid of a CNN and the EnKF is capable of reducing analysis and background errors to the same level as the QPEns. </p>

scholarly journals Conservation of Mass and Preservation of Positivity with Ensemble-Type Kalman Filter Algorithms

2014 ◽  
Vol 142 (2) ◽  
pp. 755-773 ◽  
Author(s):  
Tijana Janjić ◽  
Dennis McLaughlin ◽  
Stephen E. Cohn ◽  
Martin Verlaan
Keyword(s):  
Kalman Filter ◽  
Quadratic Programming ◽  
Ensemble Kalman Filter ◽  
Positive Impact ◽  
Computationally Efficient ◽  
Sharp Feature ◽  
Ensemble Mean ◽  
Physically Based ◽  
Quadratic Programming Problems ◽  
Nonnegativity Constraints

Abstract This paper considers the incorporation of constraints to enforce physically based conservation laws in the ensemble Kalman filter. In particular, constraints are used to ensure that the ensemble members and the ensemble mean conserve mass and remain nonnegative through measurement updates. In certain situations filtering algorithms such as the ensemble Kalman filter (EnKF) and ensemble transform Kalman filter (ETKF) yield updated ensembles that conserve mass but are negative, even though the actual states must be nonnegative. In such situations if negative values are set to zero, or a log transform is introduced, the total mass will not be conserved. In this study, mass and positivity are both preserved by formulating the filter update as a set of quadratic programming problems that incorporate nonnegativity constraints. Simple numerical experiments indicate that this approach can have a significant positive impact on the posterior ensemble distribution, giving results that are more physically plausible both for individual ensemble members and for the ensemble mean. In two examples, an update that includes a nonnegativity constraint is able to properly describe the transport of a sharp feature (e.g., a triangle or cone). A number of implementation questions still need to be addressed, particularly the need to develop a computationally efficient quadratic programming update for large ensemble.

Ensemble Kalman Filter for Out of Sequence Measurement Tracking

2012 ◽  
Vol 132 (10) ◽  
pp. 1617-1625
Author(s):  
Sirichai Pornsarayouth ◽  
Masaki Yamakita
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter

Data assimilation with the weighted ensemble Kalman filter

2010 ◽  
Author(s):  
Nicolas Papadakis ◽  
Etienne Mémin ◽  
Anne Cuzol ◽  
Nicolas Gengembre
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter

scholarly journals Assimilation of D-InSAR snow depth data by an ensemble Kalman filter

2021 ◽  
Vol 14 (6) ◽  
Author(s):  
Jinming Yang ◽  
Chengzhi Li
Keyword(s):  
Remote Sensing ◽  
Kalman Filter ◽  
Water Resource ◽  
Ensemble Kalman Filter ◽  
Snow Depth ◽  
Resource Assessment ◽  
Measured Data ◽  
Hydrological Process ◽  
Depth Data ◽  
Water Resource Assessment

AbstractSnow depth mirrors regional climate change and is a vital parameter for medium- and long-term numerical climate prediction, numerical simulation of land-surface hydrological process, and water resource assessment. However, the quality of the available snow depth products retrieved from remote sensing is inevitably affected by cloud and mountain shadow, and the spatiotemporal resolution of the snow depth data cannot meet the need of hydrological research and decision-making assistance. Therefore, a method to enhance the accuracy of snow depth data is urgently required. In the present study, three kinds of snow depth data which included the D-InSAR data retrieved from the remote sensing images of Sentinel-1 synthetic aperture radar, the automatically measured data using ultrasonic snow depth detectors, and the manually measured data were assimilated based on ensemble Kalman filter. The assimilated snow depth data were spatiotemporally consecutive and integrated. Under the constraint of the measured data, the accuracy of the assimilated snow depth data was higher and met the need of subsequent research. The development of ultrasonic snow depth detector and the application of D-InSAR technology in snow depth inversion had greatly alleviated the insufficiency of snow depth data in types and quantity. At the same time, the assimilation of multi-source snow depth data by ensemble Kalman filter also provides high-precision data to support remote sensing hydrological research, water resource assessment, and snow disaster prevention and control program.

scholarly journals Assimilation of Dynamic Combined Finite Discrete Element Methods Using the Ensemble Kalman Filter

2021 ◽  
Vol 11 (7) ◽  
pp. 2898
Author(s):  
Humberto C. Godinez ◽  
Esteban Rougier
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Failure Modes ◽  
Split Hopkinson Pressure Bar ◽  
Peak Stress ◽  
Discrete Element ◽  
Material Behavior ◽  
Model Parameters ◽  
Hopkinson Pressure Bar ◽  
Parameter Values

Simulation of fracture initiation, propagation, and arrest is a problem of interest for many applications in the scientific community. There are a number of numerical methods used for this purpose, and among the most widely accepted is the combined finite-discrete element method (FDEM). To model fracture with FDEM, material behavior is described by specifying a combination of elastic properties, strengths (in the normal and tangential directions), and energy dissipated in failure modes I and II, which are modeled by incorporating a parameterized softening curve defining a post-peak stress-displacement relationship unique to each material. In this work, we implement a data assimilation method to estimate key model parameter values with the objective of improving the calibration processes for FDEM fracture simulations. Specifically, we implement the ensemble Kalman filter assimilation method to the Hybrid Optimization Software Suite (HOSS), a FDEM-based code which was developed for the simulation of fracture and fragmentation behavior. We present a set of assimilation experiments to match the numerical results obtained for a Split Hopkinson Pressure Bar (SHPB) model with experimental observations for granite. We achieved this by calibrating a subset of model parameters. The results show a steady convergence of the assimilated parameter values towards observed time/stress curves from the SHPB observations. In particular, both tensile and shear strengths seem to be converging faster than the other parameters considered.

scholarly journals Parameters Estimation and Prediction of Water Movement and Solute Transport in Layered, Variably Saturated Soils Using the Ensemble Kalman Filter

Water ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 1520
Author(s):  
Zheng Jiang ◽  
Quanzhong Huang ◽  
Gendong Li ◽  
Guangyong Li
Keyword(s):  
Kalman Filter ◽  
Solute Transport ◽  
Ensemble Kalman Filter ◽  
Water Movement ◽  
Parameters Estimation ◽  
Saturated Soils ◽  
Hydrological Models ◽  
State Variables ◽  
Ensemble Size ◽  
Highly Nonlinear

The parameters of water movement and solute transport models are essential for the accurate simulation of soil moisture and salinity, particularly for layered soils in field conditions. Parameter estimation can be achieved using the inverse modeling method. However, this type of method cannot fully consider the uncertainties of measurements, boundary conditions, and parameters, resulting in inaccurate estimations of parameters and predictions of state variables. The ensemble Kalman filter (EnKF) is well-suited to data assimilation and parameter prediction in Situations with large numbers of variables and uncertainties. Thus, in this study, the EnKF was used to estimate the parameters of water movement and solute transport in layered, variably saturated soils. Our results indicate that when used in conjunction with the HYDRUS-1D software (University of California Riverside, California, CA, USA) the EnKF effectively estimates parameters and predicts state variables for layered, variably saturated soils. The assimilation of factors such as the initial perturbation and ensemble size significantly affected in the simulated results. A proposed ensemble size range of 50–100 was used when applying the EnKF to the highly nonlinear hydrological models of the present study. Although the simulation results for moisture did not exhibit substantial improvement with the assimilation, the simulation of the salinity was significantly improved through the assimilation of the salinity and relative solutetransport parameters. Reducing the uncertainties in measured data can improve the goodness-of-fit in the application of the EnKF method. Sparse field condition observation data also benefited from the accurate measurement of state variables in the case of EnKF assimilation. However, the application of the EnKF algorithm for layered, variably saturated soils with hydrological models requires further study, because it is a challenging and highly nonlinear problem.

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