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1.
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
2.
Edison Caballero Fernando A. Rochinha Marcio Borges Marcio A. Murad 《国际地质力学数值与分析法杂志》2019,43(2):482-500
In this work, we construct a new methodology for enhancing the predictive accuracy of sequential methods for coupling flow and geomechanics while preserving low computational cost. The new computational approach is developed within the framework of the fixed-stress split algorithm procedure in conjunction with data assimilation based on the ensemble Kalman filter (EnKF). In this context, we identify the high-fidelity model with the two-way formulation where additional source term appears in the flow equation containing the time derivative of total mean stress. The iterative scheme is then interlaced with data assimilation steps, which also incorporate the modeling error inherent to the EnKF framework. Such a procedure gives rise to an “enhanced one-way formulation,” exhibiting substantial improvement in accuracy compared with the classical one-way method. The governing equations are discretized by mixed finite elements, and numerical simulation of a 2D slab problem between injection and production wells illustrate the tremendous achievement of the method proposed herein. 相似文献
3.
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
4.
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
5.
Reza Tavakoli Gergina Pencheva Mary F. Wheeler Benjamin Ganis 《Computational Geosciences》2013,17(1):83-97
We present a parallel framework for history matching and uncertainty characterization based on the Kalman filter update equation for the application of reservoir simulation. The main advantages of ensemble-based data assimilation methods are that they can handle large-scale numerical models with a high degree of nonlinearity and large amount of data, making them perfectly suited for coupling with a reservoir simulator. However, the sequential implementation is computationally expensive as the methods require relatively high number of reservoir simulation runs. Therefore, the main focus of this work is to develop a parallel data assimilation framework with minimum changes into the reservoir simulator source code. In this framework, multiple concurrent realizations are computed on several partitions of a parallel machine. These realizations are further subdivided among different processors, and communication is performed at data assimilation times. Although this parallel framework is general and can be used for different ensemble techniques, we discuss the methodology and compare results of two algorithms, the ensemble Kalman filter (EnKF) and the ensemble smoother (ES). Computational results show that the absolute runtime is greatly reduced using a parallel implementation versus a serial one. In particular, a parallel efficiency of about 35 % is obtained for the EnKF, and an efficiency of more than 50 % is obtained for the ES. 相似文献
6.
The ensemble Kalman filter (EnKF) has been shown repeatedly to be an effective method for data assimilation in large-scale
problems, including those in petroleum engineering. Data assimilation for multiphase flow in porous media is particularly
difficult, however, because the relationships between model variables (e.g., permeability and porosity) and observations (e.g.,
water cut and gas–oil ratio) are highly nonlinear. Because of the linear approximation in the update step and the use of a
limited number of realizations in an ensemble, the EnKF has a tendency to systematically underestimate the variance of the
model variables. Various approaches have been suggested to reduce the magnitude of this problem, including the application
of ensemble filter methods that do not require perturbations to the observed data. On the other hand, iterative least-squares
data assimilation methods with perturbations of the observations have been shown to be fairly robust to nonlinearity in the
data relationship. In this paper, we present EnKF with perturbed observations as a square root filter in an enlarged state
space. By imposing second-order-exact sampling of the observation errors and independence constraints to eliminate the cross-covariance
with predicted observation perturbations, we show that it is possible in linear problems to obtain results from EnKF with
observation perturbations that are equivalent to ensemble square-root filter results. Results from a standard EnKF, EnKF with
second-order-exact sampling of measurement errors that satisfy independence constraints (EnKF (SIC)), and an ensemble square-root
filter (ETKF) are compared on various test problems with varying degrees of nonlinearity and dimensions. The first test problem
is a simple one-variable quadratic model in which the nonlinearity of the observation operator is varied over a wide range
by adjusting the magnitude of the coefficient of the quadratic term. The second problem has increased observation and model
dimensions to test the EnKF (SIC) algorithm. The third test problem is a two-dimensional, two-phase reservoir flow problem
in which permeability and porosity of every grid cell (5,000 model parameters) are unknown. The EnKF (SIC) and the mean-preserving
ETKF (SRF) give similar results when applied to linear problems, and both are better than the standard EnKF. Although the
ensemble methods are expected to handle the forecast step well in nonlinear problems, the estimates of the mean and the variance
from the analysis step for all variants of ensemble filters are also surprisingly good, with little difference between ensemble
methods when applied to nonlinear problems. 相似文献
7.
Ensemble-based data assimilation methods have recently become popular for solving reservoir history matching problems, but because of the practical limitation on ensemble size, using localization is necessary to reduce the effect of sampling error and to increase the degrees of freedom for incorporating large amounts of data. Local analysis in the ensemble Kalman filter has been used extensively for very large models in numerical weather prediction. It scales well with the model size and the number of data and is easily parallelized. In the petroleum literature, however, iterative ensemble smoothers with localization of the Kalman gain matrix have become the state-of-the-art approach for ensemble-based history matching. By forming the Kalman gain matrix row-by-row, the analysis step can also be parallelized. Localization regularizes updates to model parameters and state variables using information on the distance between the these variables and the observations. The truncation of small singular values in truncated singular value decomposition (TSVD) at the analysis step provides another type of regularization by projecting updates to dominant directions spanned by the simulated data ensemble. Typically, the combined use of localization and TSVD is necessary for problems with large amounts of data. In this paper, we compare the performance of Kalman gain localization to two forms of local analysis for parameter estimation problems with nonlocal data. The effect of TSVD with different localization methods and with the use of iteration is also analyzed. With several examples, we show that good results can be obtained for all localization methods if the localization range is chosen appropriately, but the optimal localization range differs for the various methods. In general, for local analysis with observation taper, the optimal range is somewhat shorter than the optimal range for other localization methods. Although all methods gave equivalent results when used in an iterative ensemble smoother, the local analysis methods generally converged more quickly than Kalman gain localization when the amount of data is large compared to ensemble size. 相似文献
8.
为研究观测资料稀少情况下土壤质地及有机质对土壤水分同化的影响,发展了集合卡尔曼平滑(Ensemble Kalman Smooth, EnKS)的土壤水分同化方案。利用黑河上游阿柔冻融观测站2008年6月1日至10月29日的观测数据,使用EnKS算法将表层土壤水分观测数据同化到简单生物圈模型(Simple Biosphere Model 2, SiB2)中,分析不同方案对土壤水分估计的影响,并与集合卡尔曼滤波算法(EnKF)的结果进行比较。研究结果表明,土壤质地和有机质对表层土壤水分模拟结果影响最大而对深层的影响相对较小;利用EnKF和EnKS算法同化表层土壤水分观测数据,均能够显著提高表层和根区土壤水分估计的精度,EnKS算法的精度略高于EnKF且所受土壤质地和有机质的影响小于EnKF;当观测数据稀少时,EnKS算法仍然可以得到较高精度的土壤水分估计。 相似文献
9.
重质非水相有机污染物(DNAPL)泄漏到地下后,其运移与分布特征受渗透率非均质性影响显著。为刻画DNAPL污染源区结构特征,需进行参数估计以描述水文地质参数的非均质性。本研究构建了基于集合卡尔曼滤波方法(EnKF)与多相流运移模型的同化方案,通过融合DNAPL饱和度观测数据推估非均质介质渗透率空间分布。通过二维砂箱实际与理想算例,验证了同化方法的推估效果,并探讨了不同因素对同化的影响。研究结果表明:基于EnKF方法同化饱和度观测资料可有效地推估非均质渗透率场;参数推估精度随观测时空密度的增大而提高;观测点位置分布对同化效果有所影响,布置在污染集中区域的观测数据对于参数估计具有较高的数据价值。 相似文献
10.
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
11.
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
12.
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
13.
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
14.
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
15.
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
16.
Investigation of the sampling performance of ensemble-based methods with a simple reservoir model 总被引：1，自引：0，他引：1
The application of the ensemble Kalman filter (EnKF) for history matching petroleum reservoir models has been the subject of intense investigation during the past 10 years. Unfortunately, EnKF often fails to provide reasonable data matches for highly nonlinear problems. This fact motivated the development of several iterative ensemble-based methods in the last few years. However, there exists no study comparing the performance of these methods in the literature, especially in terms of their ability to quantify uncertainty correctly. In this paper, we compare the performance of nine ensemble-based methods in terms of the quality of the data matches, quantification of uncertainty, and computational cost. For this purpose, we use a small but highly nonlinear reservoir model so that we can generate the reference posterior distribution of reservoir properties using a very long chain generated by a Markov chain Monte Carlo sampling algorithm. We also consider one adjoint-based implementation of the randomized maximum likelihood method in the comparisons. 相似文献
17.
Ensemble Kalman filtering with shrinkage regression techniques 总被引：1，自引：0，他引：1
The classical ensemble Kalman filter (EnKF) is known to underestimate the prediction uncertainty. This can potentially lead
to low forecast precision and an ensemble collapsing into a single realisation. In this paper, we present alternative EnKF
updating schemes based on shrinkage methods known from multivariate linear regression. These methods reduce the effects caused
by collinear ensemble members and have the same computational properties as the fastest EnKF algorithms previously suggested.
In addition, the importance of model selection and validation for prediction purposes is investigated, and a model selection
scheme based on cross-validation is introduced. The classical EnKF scheme is compared with the suggested procedures on two-toy
examples and one synthetic reservoir case study. Significant improvements are seen, both in terms of forecast precision and
prediction uncertainty estimates. 相似文献
18.
19.
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
20.
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