共查询到20条相似文献，搜索用时 62 毫秒
1.
In recent years, data assimilation techniques have been applied to an increasingly wider specter of problems. Monte Carlo
variants of the Kalman filter, in particular, the ensemble Kalman filter (EnKF), have gained significant popularity. EnKF
is used for a wide variety of applications, among them for updating reservoir simulation models. EnKF is a Monte Carlo method,
and its reliability depends on the actual size of the sample. In applications, a moderately sized sample (40–100 members)
is used for computational convenience. Problems due to the resulting Monte Carlo effects require a more thorough analysis
of the EnKF. Earlier we presented a method for the assessment of the error emerging at the EnKF update step (Kovalenko et
al., SIAM J Matrix Anal Appl, in press). A particular energy norm of the EnKF error after a single update step was studied.
The energy norm used to assess the error is hard to interpret. In this paper, we derive the distribution of the Euclidean
norm of the sampling error under the same assumptions as before, namely normality of the forecast distribution and negligibility
of the observation error. The distribution depends on the ensemble size, the number and spatial arrangement of the observations,
and the prior covariance. The distribution is used to study the error propagation in a single update step on several synthetic
examples. The examples illustrate the changes in reliability of the EnKF, when the parameters governing the error distribution
vary. 相似文献
2.
Wiktoria Lawniczak Remus Hanea Arnold Heemink Dennis McLaughlin 《Computational Geosciences》2009,13(2):245-254
Reservoir management requires periodic updates of the simulation models using the production data available over time. Traditionally,
validation of reservoir models with production data is done using a history matching process. Uncertainties in the data, as
well as in the model, lead to a nonunique history matching inverse problem. It has been shown that the ensemble Kalman filter
(EnKF) is an adequate method for predicting the dynamics of the reservoir. The EnKF is a sequential Monte-Carlo approach that
uses an ensemble of reservoir models. For realistic, large-scale applications, the ensemble size needs to be kept small due
to computational inefficiency. Consequently, the error space is not well covered (poor cross-correlation matrix approximations)
and the updated parameter field becomes scattered and loses important geological features (for example, the contact between
high- and low-permeability values). The prior geological knowledge present in the initial time is not found anymore in the
final updated parameter. We propose a new approach to overcome some of the EnKF limitations. This paper shows the specifications
and results of the ensemble multiscale filter (EnMSF) for automatic history matching. EnMSF replaces, at each update time,
the prior sample covariance with a multiscale tree. The global dependence is preserved via the parent–child relation in the
tree (nodes at the adjacent scales). After constructing the tree, the Kalman update is performed. The properties of the EnMSF
are presented here with a 2D, two-phase (oil and water) small twin experiment, and the results are compared to the EnKF. The
advantages of using EnMSF are localization in space and scale, adaptability to prior information, and efficiency in case many
measurements are available. These advantages make the EnMSF a practical tool for many data assimilation problems. 相似文献
3.
The ensemble Kalman filter (EnKF), an efficient data assimilation method showing advantages in many numerical experiments, is deficient when used in approximating covariance from an ensemble of small size. Implicit localization is used to add distance-related weight to covariance and filter spurious correlations which weaken the EnKF??s capability to estimate uncertainty correctly. The effect of this kind of localization is studied in two-dimensional (2D) and three-dimensional (3D) synthetic cases. It is found that EnKF with localization can capture reliably both the mean and variance of the hydraulic conductivity field with higher efficiency; it can also greatly stabilize the assimilation process as a small-size ensemble is used. Sensitivity experiments are conducted to explore the effect of localization function format and filter lengths. It is suggested that too long or too short filter lengths will prevent implicit localization from modifying the covariance appropriately. Steep localization functions will greatly disturb local dynamics like the 0-1 function even if the function is continuous; four relatively gentle localization functions succeed in avoiding obvious disturbance to the system and improve estimation. As the degree of localization of the L function increases, the parameter sensitivity becomes weak, making parameter selection easier, but more information may be lost in the assimilation process. 相似文献
4.
Andreas S. Stordal Randi Valestrand Hans Arnfinn Karlsen Geir N?vdal Hans Julius Skaug 《Computational Geosciences》2012,16(2):467-482
Over the last years, the ensemble Kalman filter (EnKF) has become a very popular tool for history matching petroleum reservoirs.
EnKF is an alternative to more traditional history matching techniques as it is computationally fast and easy to implement.
Instead of seeking one best model estimate, EnKF is a Monte Carlo method that represents the solution with an ensemble of
state vectors. Lately, several ensemble-based methods have been proposed to improve upon the solution produced by EnKF. In
this paper, we compare EnKF with one of the most recently proposed methods, the adaptive Gaussian mixture filter (AGM), on
a 2D synthetic reservoir and the Punq-S3 test case. AGM was introduced to loosen up the requirement of a Gaussian prior distribution
as implicitly formulated in EnKF. By combining ideas from particle filters with EnKF, AGM extends the low-rank kernel particle
Kalman filter. The simulation study shows that while both methods match the historical data well, AGM is better at preserving
the geostatistics of the prior distribution. Further, AGM also produces estimated fields that have a higher empirical correlation
with the reference field than the corresponding fields obtained with EnKF. 相似文献
5.
集合卡曼滤波由于易于使用而被广泛地应用到陆面数据同化研究中,它是建立在模型为线性、误差为正态分布的假设上,而实际土壤湿度方程是高度非线性的,并且当土壤过干或过湿时会发生样本偏斜.为了全面评估它在同化表层土壤湿度观测来反演土壤湿度廓线的性能,特引入不需要上述假设的采样重要性重采样粒子滤波,比较非线性和偏斜性对同化算法的影响.结果显示:不管是小样本还是大样本,集合卡曼滤波都能快速、准确地逼近样本均值,而粒子滤波只有在大样本时才能缓慢地趋近;此外,集合卡曼滤波的粒子边缘概率密度及其偏度和峰度与粒子滤波完全不同,前者粒子虽不完全满足正态分布,但始终为单峰状态,而后者粒子随同化推进经历了单峰到双峰再到单峰的变化. 相似文献
6.
集合卡尔曼滤波(Ensemble Kalman Filter,EnKF)作为一种有效的数据同化方法,在众多数值实验中体现优势的同时,也暴露了它使用小集合估计协方差情况下精度较低的缺陷。为了降低取样噪声对协方差估计的干扰并提高滤波精度,应用局域化函数对小集合估计的协方差进行修正,即在协方差矩阵中以舒尔积的形式增加空间距离权重以限制远距离相关。在一个二维理想孔隙承压含水层模型中的运行结果表明,局域化对集合卡尔曼滤波估计地下水参数的修正十分有效,局域化可以很好地过滤小集合估计中噪声的影响,节省计算量的同时又可以防止滤波发散。相关长度较小的水文地质参数(如对数渗透系数)更容易受到噪声的干扰,更有必要进行局域化修正。 相似文献
7.
Mohammadali Tarrahi Siavash Hakim Elahi Behnam Jafarpour 《Computational Geosciences》2016,20(5):929-952
Ensemble methods present a practical framework for parameter estimation, performance prediction, and uncertainty quantification in subsurface flow and transport modeling. In particular, the ensemble Kalman filter (EnKF) has received significant attention for its promising performance in calibrating heterogeneous subsurface flow models. Since an ensemble of model realizations is used to compute the statistical moments needed to perform the EnKF updates, large ensemble sizes are needed to provide accurate updates and uncertainty assessment. However, for realistic problems that involve large-scale models with computationally demanding flow simulation runs, the EnKF implementation is limited to small-sized ensembles. As a result, spurious numerical correlations can develop and lead to inaccurate EnKF updates, which tend to underestimate or even eliminate the ensemble spread. Ad hoc practical remedies, such as localization, local analysis, and covariance inflation schemes, have been developed and applied to reduce the effect of sampling errors due to small ensemble sizes. In this paper, a fast linear approximate forecast method is proposed as an alternative approach to enable the use of large ensemble sizes in operational settings to obtain more improved sample statistics and EnKF updates. The proposed method first clusters a large number of initial geologic model realizations into a small number of groups. A representative member from each group is used to run a full forward flow simulation. The flow predictions for the remaining realizations in each group are approximated by a linearization around the full simulation results of the representative model (centroid) of the respective cluster. The linearization can be performed using either adjoint-based or ensemble-based gradients. Results from several numerical experiments with two-phase and three-phase flow systems in this paper suggest that the proposed method can be applied to improve the EnKF performance in large-scale problems where the number of full simulation is constrained. 相似文献
8.
In this work, we present an efficient matrix-free ensemble Kalman filter (EnKF) algorithm for the assimilation of large data
sets. The EnKF has increasingly become an essential tool for data assimilation of numerical models. It is an attractive assimilation
method because it can evolve the model covariance matrix for a non-linear model, through the use of an ensemble of model states,
and it is easy to implement for any numerical model. Nevertheless, the computational cost of the EnKF can increase significantly
for cases involving the assimilation of large data sets. As more data become available for assimilation, a potential bottleneck
in most EnKF algorithms involves the operation of the Kalman gain matrix. To reduce the complexity and cost of assimilating
large data sets, a matrix-free EnKF algorithm is proposed. The algorithm uses an efficient matrix-free linear solver, based
on the Sherman–Morrison formulas, to solve the implicit linear system within the Kalman gain matrix and compute the analysis.
Numerical experiments with a two-dimensional shallow water model on the sphere are presented, where results show the matrix-free
implementation outperforming an singular value decomposition-based implementation in computational time. 相似文献
9.
Continuous Facies Updating Using the Ensemble Kalman Filter and the Level Set Method 总被引：1，自引：1，他引：0
We present a methodology based on the ensemble Kalman filter (EnKF) and the level set method for the continuous model updating of geological facies with respect to production data. Geological facies are modeled using an implicit surface representation and conditioned to production data using the ensemble Kalman filter. The methodology is based on Gaussian random fields used to deform the facies boundaries. The Gaussian random fields are used as the model parameter vector to be updated sequentially within the EnKF when new measurements are available. We show the successful application of the methodology to two synthetic reservoir models. 相似文献
10.
利用1998年7月6日至8月9日青藏高原GAME-Tibet试验区MS3608站点的4cm、20cm和100cm的土壤水分观测数据同化SiB2模型输出的表层、根区和深层土壤水分,探讨了一个基于集合卡尔曼滤波和简单生物圈模型的单点土壤水分同化方案。分析和评价了集合大小、同化周期、模型误差、背景场误差以及观测误差对同化系统性能的影响。结果表明:①增加集合数目可以减小土壤水分同化系统的误差,但同时又降低了运行效率;②对于集合卡尔曼滤波,初始场的估计是否准确对同化系统性能影响不大;③模型误差和观测误差的准确估计可以提高土壤水分的估计精度;④利用数据同化的方法对土壤水分的估计有显著提高。 相似文献
11.
Combining sensitivities and prior information for covariance localization in the ensemble Kalman filter for petroleum reservoir applications 总被引：1，自引：0，他引：1
Sampling errors can severely degrade the reliability of estimates of conditional means and uncertainty quantification obtained
by the application of the ensemble Kalman filter (EnKF) for data assimilation. A standard recommendation for reducing the
spurious correlations and loss of variance due to sampling errors is to use covariance localization. In distance-based localization,
the prior (forecast) covariance matrix at each data assimilation step is replaced with the Schur product of a correlation
matrix with compact support and the forecast covariance matrix. The most important decision to be made in this localization
procedure is the choice of the critical length(s) used to generate this correlation matrix. Here, we give a simple argument
that the appropriate choice of critical length(s) should be based both on the underlying principal correlation length(s) of
the geological model and the range of the sensitivity matrices. Based on this result, we implement a procedure for covariance
localization and demonstrate with a set of distinctive reservoir history-matching examples that this procedure yields improved
results over the standard EnKF implementation and over covariance localization with other choices of critical length. 相似文献
12.
We present a method of using classical wavelet-based multiresolution analysis to separate scales in model and observations during data assimilation with the ensemble Kalman filter. In many applications, the underlying physics of a phenomena involve the interaction of features at multiple scales. Blending of observational and model error across scales can result in large forecast inaccuracies since large errors at one scale are interpreted as inexact data at all scales due to the misrepresentation of observational error. Our method uses a partitioning of the range of the observation operator into separate observation scales. This naturally induces a transformation of the observation covariance and we put forward several algorithms to efficiently compute the transformed covariance. Another advantage of our multiresolution ensemble Kalman filter is that scales can be weighted independently to adjust each scale’s affect on the forecast. To demonstrate feasibility, we present applications to a one-dimensional Kuramoto-Sivashinsky (K–S) model with scale-dependent observation noise and an application involving the forecasting of solar photospheric flux. The solar flux application uses the Air Force Data Assimilative Photospheric Transport (ADAPT) model which has model and observation error exhibiting strong scale dependence. Results using our multiresolution ensemble Kalman filter show significant improvement in solar forecast error compared to traditional ensemble Kalman filtering. 相似文献
13.
Relation between two common localisation methods for the EnKF 总被引：3，自引：0，他引：3
This study investigates the relation between two common localisation methods in ensemble Kalman filter (EnKF) systems: covariance
localisation and local analysis. Both methods are popular in large-scale applications with the EnKF. The case of local observations
with non-correlated errors is considered. Both methods are formulated in terms of tapering of ensemble anomalies, which provides
a framework for their comparison. Based on analytical considerations and experimental evidence, we conclude that in practice
the two methods should yield very similar results, so that the choice between them should be based on other criteria, such
as numerical effectiveness and scalability. 相似文献
14.
Using a small ensemble size in the ensemble Kalman filter methodology is efficient for updating numerical reservoir models
but can result in poor updates following spurious correlations between observations and model variables. The most common approach
for reducing the effect of spurious correlations on model updates is multiplication of the estimated covariance by a tapering
function that eliminates all correlations beyond a prespecified distance. Distance-dependent tapering is not always appropriate,
however. In this paper, we describe efficient methods for discriminating between the real and the spurious correlations in
the Kalman gain matrix by using the bootstrap method to assess the confidence level of each element from the Kalman gain matrix.
The new method is tested on a small linear problem, and on a water flooding reservoir history matching problem. For the water
flooding example, a small ensemble size of 30 was used to compute the Kalman gain in both the screened EnKF and standard EnKF
methods. The new method resulted in significantly smaller root mean squared errors of the estimated model parameters and greater
variability in the final updated ensemble. 相似文献
15.
The ensemble Kalman filter has been successfully applied for data assimilation in very large models, including those in reservoir
simulation and weather. Two problems become critical in a standard implementation of the ensemble Kalman filter, however,
when the ensemble size is small. The first is that the ensemble approximation to cross-covariances of model and state variables
to data can indicate the presence of correlations that are not real. These spurious correlations give rise to model or state
variable updates in regions that should not be updated. The second problem is that the number of degrees of freedom in the
ensemble is only as large as the size of the ensemble, so the assimilation of large amounts of precise, independent data is
impossible. Localization of the Kalman gain is almost universal in the weather community, but applications of localization
for the ensemble Kalman filter in porous media flow have been somewhat rare. It has been shown, however, that localization
of updates to regions of non-zero sensitivity or regions of non-zero cross-covariance improves the performance of the EnKF
when the ensemble size is small. Localization is necessary for assimilation of large amounts of independent data. The problem
is to define appropriate localization functions for different types of data and different types of variables. We show that
the knowledge of sensitivity alone is not sufficient for determination of the region of localization. The region depends also
on the prior covariance for model variables and on the past history of data assimilation. Although the goal is to choose localization
functions that are large enough to include the true region of non-zero cross-covariance, for EnKF applications, the choice
of localization function needs to balance the harm done by spurious covariance resulting from small ensembles and the harm
done by excluding real correlations. In this paper, we focus on the distance-based localization and provide insights for choosing
suitable localization functions for data assimilation in multiphase flow problems. In practice, we conclude that it is reasonable
to choose localization functions based on well patterns, that localization function should be larger than regions of non-zero
sensitivity and should extend beyond a single well pattern. 相似文献
16.
In this paper we present an extension of the ensemble Kalman filter (EnKF) specifically designed for multimodal systems. EnKF
data assimilation scheme is less accurate when it is used to approximate systems with multimodal distribution such as reservoir
facies models. The algorithm is based on the assumption that both prior and posterior distribution can be approximated by
Gaussian mixture and it is validated by the introduction of the concept of finite ensemble representation. The effectiveness
of the approach is shown with two applications. The first example is based on Lorenz model. In the second example, the proposed
methodology combined with a localization technique is used to update a 2D reservoir facies models. Both applications give
evidence of an improved performance of the proposed method respect to the EnKF. 相似文献
17.
集合—变分数据同化方法的发展与应用 总被引：3，自引：0，他引：3
近年来,集合—变分数据同化方法已成为大气数据同化领域研究的热点问题.该方法能够综合利用集合卡尔曼滤波和变分同化的优势,是实现“集合预报和数据同化一体化”的有效途径.在分析变分同化和集合卡尔曼滤波优缺点的基础上引出集合—变分数据同化的概念;按照不同实现方式,将集合—变分同化分为协方差线性组合和增加控制变量2类,介绍了相应的研究进展,并将集合—变分同化概念拓展;然后介绍了集合—变分同化在英美两国的应用;最后回顾了集合—变分同化研究的主要问题,展望了未来的发展趋势. 相似文献
18.
This paper proposes an augmented Lagrangian method for production optimization in which the cost function to be maximized
is defined as an augmented Lagrangian function consisting of the net present value (NPV) and all the equality and inequality
constraints except the bound constraints. The bound constraints are dealt with using a trust-region gradient projection method.
The paper also presents a way to eliminate the need to convert the inequality constraints to equality constraints with slack
variables in the augmented Lagrangian function, which greatly reduces the size of the optimization problem when the number
of inequality constraints is large. The proposed method is tested in the context of closed-loop reservoir management benchmark
problem based on the Brugge reservoir setup by TNO. In the test, we used the ensemble Kalman filter (EnKF) with covariance
localization for data assimilation. Production optimization is done on the updated ensemble mean model from EnKF. The production
optimization resulted in a substantial increase in the NPV for the expected reservoir life compared to the base case with
reactive control. 相似文献
19.
The study has been focused on examining the usage and the applicability of ensemble Kalman filtering techniques to the history
matching procedures. The ensemble Kalman filter (EnKF) is often applied nowadays to solving such a problem. Meanwhile, traditional
EnKF requires assumption of the distribution’s normality. Besides, it is based on the linear update of the analysis equations.
These facts may cause problems when filter is used in reservoir applications and result in sampling error. The situation becomes
more problematic if the a priori information on the reservoir structure is poor and initial guess about the, e.g., permeability
field is far from the actual one. The above circumstance explains a reason to perform some further research concerned with
analyzing specific modification of the EnKF-based approach, namely, the iterative EnKF (IEnKF) scheme, which allows restarting
the procedure with a new initial guess that is closer to the actual solution and, hence, requires less improvement by the
algorithm while providing better estimation of the parameters. The paper presents some examples for which the IEnKF algorithm
works better than traditional EnKF. The algorithms are compared while estimating the permeability field in relation to the
two-phase, two-dimensional fluid flow model. 相似文献
20.
The ensemble Kalman filter (EnKF) has become a popular method for history matching production and seismic data in petroleum
reservoir models. However, it is known that EnKF may fail to give acceptable data matches especially for highly nonlinear
problems. In this paper, we introduce a procedure to improve EnKF data matches based on assimilating the same data multiple
times with the covariance matrix of the measurement errors multiplied by the number of data assimilations. We prove the equivalence
between single and multiple data assimilations for the linear-Gaussian case and present computational evidence that multiple
data assimilations can improve EnKF estimates for the nonlinear case. The proposed procedure was tested by assimilating time-lapse
seismic data in two synthetic reservoir problems, and the results show significant improvements compared to the standard EnKF.
In addition, we review the inversion schemes used in the EnKF analysis and present a rescaling procedure to avoid loss of
information during the truncation of small singular values. 相似文献