scholarly journals Assessment of multilevel ensemble-based data assimilation for reservoir history matching

2019 ◽  
Vol 24 (1) ◽  
pp. 217-239
Author(s):  
Kristian Fossum ◽  
Trond Mannseth ◽  
Andreas S. Stordal
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
History Matching ◽  
Computational Cost ◽  
Ensemble Size ◽  
Matching Problems ◽  
Reservoir Models ◽  
Reservoir History Matching ◽  
Computational Resources

AbstractMultilevel ensemble-based data assimilation (DA) as an alternative to standard (single-level) ensemble-based DA for reservoir history matching problems is considered. Restricted computational resources currently limit the ensemble size to about 100 for field-scale cases, resulting in large sampling errors if no measures are taken to prevent it. With multilevel methods, the computational resources are spread over models with different accuracy and computational cost, enabling a substantially increased total ensemble size. Hence, reduced numerical accuracy is partially traded for increased statistical accuracy. A novel multilevel DA method, the multilevel hybrid ensemble Kalman filter (MLHEnKF) is proposed. Both the expected and the true efficiency of a previously published multilevel method, the multilevel ensemble Kalman filter (MLEnKF), and the MLHEnKF are assessed for a toy model and two reservoir models. A multilevel sequence of approximations is introduced for all models. This is achieved via spatial grid coarsening and simple upscaling for the reservoir models, and via a designed synthetic sequence for the toy model. For all models, the finest discretization level is assumed to correspond to the exact model. The results obtained show that, despite its good theoretical properties, MLEnKF does not perform well for the reservoir history matching problems considered. We also show that this is probably caused by the assumptions underlying its theoretical properties not being fulfilled for the multilevel reservoir models considered. The performance of MLHEnKF, which is designed to handle restricted computational resources well, is quite good. Furthermore, the toy model is utilized to set up a case where the assumptions underlying the theoretical properties of MLEnKF are fulfilled. On that case, MLEnKF performs very well and clearly better than MLHEnKF.

scholarly journals Parallel Implementation of the Deterministic Ensemble Kalman Filter for Reservoir History Matching

Processes ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1980
Author(s):  
Lihua Shen ◽  
Hui Liu ◽  
Zhangxin Chen
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Message Passing ◽  
History Matching ◽  
Message Passing Interface ◽  
Parallel Implementation ◽  
Computational Time ◽  
Ensemble Size ◽  
Three Phase ◽  
Reservoir History Matching

In this paper, the deterministic ensemble Kalman filter is implemented with a parallel technique of the message passing interface based on our in-house black oil simulator. The implementation is separated into two cases: (1) the ensemble size is greater than the processor number and (2) the ensemble size is smaller than or equal to the processor number. Numerical experiments for estimations of three-phase relative permeabilities represented by power-law models with both known endpoints and unknown endpoints are presented. It is shown that with known endpoints, good estimations can be obtained. With unknown endpoints, good estimations can still be obtained using more observations and a larger ensemble size. Computational time is reported to show that the run time is greatly reduced with more CPU cores. The MPI speedup is over 70% for a small ensemble size and 77% for a large ensemble size with up to 640 CPU cores.

scholarly journals Optimal ensemble size of ensemble Kalman filter in sequential soil moisture data assimilation

2015 ◽  
Vol 42 (16) ◽  
pp. 6710-6715 ◽  
Author(s):  
Jifu Yin ◽  
Xiwu Zhan ◽  
Youfei Zheng ◽  
Christopher R. Hain ◽  
Jicheng Liu ◽  
...  
Keyword(s):  
Soil Moisture ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Ensemble Size ◽  
Soil Moisture Data ◽  
Optimal Ensemble

A Probabilistic Collocation-Based Kalman Filter for History Matching

SPE Journal ◽  
2011 ◽  
Vol 16 (02) ◽  
pp. 294-306 ◽  
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.

Data Assimilation for Strongly Nonlinear Problems by Transformed Ensemble Kalman Filter

SPE Journal ◽  
2014 ◽  
Vol 20 (01) ◽  
pp. 202-221 ◽  
Author(s):  
Qinzhuo Liao ◽  
Dongxiao Zhang
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
History Matching ◽  
Homogeneous Medium ◽  
Forward Model ◽  
Dynamic State ◽  
Initial Time ◽  
Static State ◽  
Strongly Nonlinear

Summary The ensemble Kalman filter (EnKF) has been widely used for data assimilation. It is challenging, however, when the relation of state and observation is strongly nonlinear. For example, near the flooding front in an immiscible flow, directly updating the saturation by use of the EnKF may lead to nonphysical results. One possible solution, which may be referred to as the restarted EnKF (REnKF), is to update the static state (e.g., permeability and porosity) and rerun the forward model from the initial time to obtain the updated dynamic state (e.g., pressure and saturation). However, it may become time-consuming, especially when the number of assimilation steps is large. In this study, we develop a transformed EnKF (TEnKF), in which the state is represented by displacement as an alternative variable. The displacement is first transformed from the forecasted state, then updated, and finally transformed back to obtain the updated state. Because the relation between displacement and observation is relatively linear, this new method provides a physically meaningful updated state without resolving the forward model. The TEnKF is tested in the history matching of multiphase flow in a 1D homogeneous medium, a 2D heterogeneous reservoir, and a 3D PUNQ-S3 model. The case studies show that the TEnKF produces physical results without the oscillation problem that occurs in the traditional EnKF, whereas the computational effort is reduced compared with the REnKF.

scholarly journals History matching of petroleum reservoir models by the Ensemble Kalman Filter and parameterization methods

2013 ◽  
Vol 55 ◽  
pp. 84-95 ◽  
Author(s):  
Leila Heidari ◽  
Véronique Gervais ◽  
Mickaële Le Ravalec ◽  
Hans Wackernagel
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
History Matching ◽  
Petroleum Reservoir ◽  
Reservoir Models

Use of Phase Streamlines for Covariance Localization in Ensemble Kalman Filter for Three-Phase History Matching

2012 ◽  
Vol 15 (03) ◽  
pp. 273-289 ◽  
Author(s):  
Shingo Watanabe ◽  
Akhil Datta-Gupta
Keyword(s):  
Kalman Filter ◽  
Gas Phase ◽  
Ensemble Kalman Filter ◽  
History Matching ◽  
Model Parameters ◽  
Ensemble Size ◽  
Three Phase ◽  
Cross Covariance ◽  
The Cross ◽  
Water Cut

Summary The ensemble Kalman filter (EnKF) has gained increased popularity for history matching and continuous reservoir-model updating. It is a sequential Monte Carlo approach that works with an ensemble of reservoir models. Specifically, the method uses cross covariance between measurements and model parameters estimated from the ensemble. For practical field applications, the ensemble size needs to be kept small for computational efficiency. However, this leads to poor approximations of the cross covariance and can cause loss of geologic realism from unrealistic model updates outside the region of the data influence and/or loss of variance leading to ensemble collapse. A common approach to remedy the situation is to limit the influence of the data through covariance localization. In this paper, we show that for three-phase-flow conditions, the region of covariance localization strongly depends on the underlying flow dynamics as well as on the particular data type that is being assimilated, for example, water cut or gas/oil ratio (GOR). This makes the traditional distance-based localizations suboptimal and, often, ineffective. Instead, we propose the use of water- and gas-phase streamlines as a means for covariance localization for water-cut- and GOR-data assimilation. The phase streamlines can be computed on the basis of individual-phase velocities which are readily available after flow simulation. Unlike the total velocity streamlines, phase streamlines can be discontinuous. We show that the discontinuities in water-phase and gas-phase streamlines naturally define the region of influence for water-cut and GOR data and provide a flow-relevant covariance localization during EnKF updating. We first demonstrate the validity of the proposed localization approach using a waterflood example in a quarter-five-spot pattern. Specifically, we compare the phase streamline trajectories with cross-covariance maps computed using an ensemble size of 2,000 for both water-cut and GOR data. The results show a close correspondence between the time evolution of phase streamlines and the cross-covariance maps of water-cut and GOR data. A benchmark uncertainty quantification (the PUNQ-S3) (Carter 2007) model application shows that our proposed localization outperforms the distance-based localization method. The updated models show improved forecasts while preserving geologic realism.

scholarly journals Uncertainty Quantification in Reservoir History Matching Using the Ensemble Smoother

2019 ◽  
Author(s):  
Thiago M. D. Silva ◽  
Abelardo Barreto ◽  
Sinesio Pesco
Keyword(s):  
Data Assimilation ◽  
Uncertainty Quantification ◽  
History Matching ◽  
Computational Cost ◽  
Nonlinear Problems ◽  
Good Alternative ◽  
Multiple Data ◽  
Ensemble Smoother ◽  
Reservoir History Matching ◽  
Low Computational Cost

Ensemble-based methods have been widely used in uncertainty quantification, particularly, in reservoir history matching. The search for a more robust method which holds high nonlinear problems is the focus for this area. The Ensemble Kalman Filter (EnKF) is a popular tool for these problems, but studies have noticed uncertainty in the results of the final ensemble, high dependent on the initial ensemble. The Ensemble Smoother (ES) is an alternative, with an easier impletation and low computational cost. However, it presents the same problem as the EnKF. The Ensemble Smoother with Multiple Data Assimilation (ES-MDA) seems to be a good alternative to these ensemble-based methods, once it assimilates tha same data multiple times. In this work, we analyze the efficiency of the Ensemble Smoother and the Ensemble Smoother with multiple data assimilation in a reservoir histoy matching of a turbidite model with 3 layers, considering permeability estimation and data mismatch.

scholarly journals Towards predictive data-driven simulations of wildfire spread – Part I: Reduced-cost Ensemble Kalman Filter based on a Polynomial Chaos surrogate model for parameter estimation

2014 ◽  
Vol 2 (5) ◽  
pp. 3289-3349 ◽  
Author(s):  
M. C. Rochoux ◽  
S. Ricci ◽  
D. Lucor ◽  
B. Cuenot ◽  
A. Trouvé
Keyword(s):  
Parameter Estimation ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Polynomial Chaos ◽  
Computational Cost ◽  
Fire Spread ◽  
Data Driven ◽  
Fire Front ◽  
Wildfire Spread

Abstract. This paper is the first part in a series of two articles and presents a data-driven wildfire simulator for forecasting wildfire spread scenarios, at a reduced computational cost that is consistent with operational systems. The prototype simulator features the following components: a level-set-based fire propagation solver FIREFLY that adopts a regional-scale modeling viewpoint, treats wildfires as surface propagating fronts, and uses a description of the local rate of fire spread (ROS) as a function of environmental conditions based on Rothermel's model; a series of airborne-like observations of the fire front positions; and a data assimilation algorithm based on an ensemble Kalman filter (EnKF) for parameter estimation. This stochastic algorithm partly accounts for the non-linearities between the input parameters of the semi-empirical ROS model and the fire front position, and is sequentially applied to provide a spatially-uniform correction to wind and biomass fuel parameters as observations become available. A wildfire spread simulator combined with an ensemble-based data assimilation algorithm is therefore a promising approach to reduce uncertainties in the forecast position of the fire front and to introduce a paradigm-shift in the wildfire emergency response. In order to reduce the computational cost of the EnKF algorithm, a surrogate model based on a polynomial chaos (PC) expansion is used in place of the forward model FIREFLY in the resulting hybrid PC-EnKF algorithm. The performance of EnKF and PC-EnKF is assessed on synthetically-generated simple configurations of fire spread to provide valuable information and insight on the benefits of the PC-EnKF approach as well as on a controlled grassland fire experiment. The results indicate that the proposed PC-EnKF algorithm features similar performance to the standard EnKF algorithm, but at a much reduced computational cost. In particular, the re-analysis and forecast skills of data assimilation strongly relate to the spatial and temporal variability of the errors in the ROS model parameters.

Using the (3N)-dimensional generalized Lorenz systems as a testbed for data assimilation: The ensemble Kalman filter

2021 ◽  
Author(s):  
Sungju Moon ◽  
Jong-Jin Baik
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Lorenz System ◽  
Ensemble Size ◽  
Flexible Tool ◽  
Generalized System ◽  
Generalized Lorenz System ◽  
The Lorenz System ◽  
True System

AbstractThe feasibility of using a (3N)-dimensional generalization of the Lorenz system in testing a traditional implementation of the ensemble Kalman filter is explored through numerical experiments. The generalization extends the Lorenz system, known as the Lorenz ’63 model, into a (3N)-dimensional nonlinear system for any positive integer N. Because the extension involves inclusion of additional wavenumber modes, raising the dimension allows the system to resolve smaller-scale motions, a unique characteristic of the present generalization that can be relevant to real modeling scenarios. Model imperfections are simulated by assuming a high-dimensional generalized Lorenz system as the true system and a generalized system of dimension less than or equal to the dimension of the true system as the model system. Different scenarios relevant to data assimilation practices are simulated by varying the dimensional-differences between the model and true systems, ensemble size, and observation frequency and accuracy. It is suggested that the present generalization of the Lorenz system is an interesting and flexible tool for evaluating the effectiveness of data assimilation methods and a meaningful addition to the portfolio of testbed systems that includes the Lorenz ’63 and ’96 models, especially considering its relationship with the Lorenz ’63 model. The results presented in this study can serve as useful benchmarks for testing other data assimilation methods besides the ensemble Kalman filter.

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