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1.
A probabilistic parametrization for geological uncertainty estimation using the ensemble Kalman filter (EnKF) 总被引：2，自引：0，他引：2
In the past years, many applications of history-matching methods in general and ensemble Kalman filter in particular have been proposed, especially in order to estimate fields that provide uncertainty in the stochastic process defined by the dynamical system of hydrocarbon recovery. Such fields can be permeability fields or porosity fields, but can also fields defined by the rock type (facies fields). The estimation of the boundaries of the geologic facies with ensemble Kalman filter (EnKF) was made, in different papers, with the aid of Gaussian random fields, which were truncated using various schemes and introduced in a history-matching process. In this paper, we estimate, in the frame of the EnKF process, the locations of three facies types that occur into a reservoir domain, with the property that each two could have a contact. The geological simulation model is a form of the general truncated plurigaussian method. The difference with other approaches consists in how the truncation scheme is introduced and in the observation operator of the facies types at the well locations. The projection from the continuous space of the Gaussian fields into the discrete space of the facies fields is realized through in an intermediary space (space with probabilities). This space connects the observation operator of the facies types at the well locations with the geological simulation model. We will test the model using a 2D reservoir which is connected with the EnKF method as a data assimilation technique. We will use different geostatistical properties for the Gaussian fields and different levels of the uncertainty introduced in the model parameters and also in the construction of the Gaussian fields. 相似文献
2.
The prediction of fluid flows within hydrocarbon reservoirs requires the characterization of petrophysical properties. Such characterization is performed on the basis of geostatistics and history-matching; in short, a reservoir model is first randomly drawn, and then sequentially adjusted until it reproduces the available dynamic data. Two main concerns typical of the problem under consideration are the heterogeneity of rocks occurring at all scales and the use of data of distinct resolution levels. Therefore, referring to sequential Gaussian simulation, this paper proposes a new stochastic simulation method able to handle several scales for both continuous or discrete random fields. This method adds flexibility to history-matching as it boils down to the multiscale parameterization of reservoir models. In other words, reservoir models can be updated at either coarse or fine scales, or both. Parameterization adapts to the available data; the coarser the scale targeted, the smaller the number of unknown parameters, and the more efficient the history-matching process. This paper focuses on the use of variational optimization techniques driven by the gradual deformation method to vary reservoir models. Other data assimilation methods and perturbation processes could have been envisioned as well. Last, a numerical application case is presented in order to highlight the advantages of the proposed method for conditioning permeability models to dynamic data. For simplicity, we focus on two-scale processes. The coarse scale describes the variations in the trend while the fine scale characterizes local variations around the trend. The relationships between data resolution and parameterization are investigated. 相似文献
3.
M. Le Ravalec-Dupin L. Y. Hu F. Roggero 《地学前缘》2008,15(1):176-186
计算机能力的提升和历史拟合方面的最新进展促进了对先前建立的储层模型的重新检验。为了节省工程师和CPU的时间,我们开发了4种独特的算法,来允许无需重新进行储层研究而重建现有模型。这些算法涉及的技术包括:优化、松弛、Wiener滤波或序贯重构。基本上,它们被用来确定一个随机函数和一系列随机数。给定一个随机函数,一族随机数将产生一个实现,这个实现和现有的储层模型十分接近。一旦随机数已知,现有的储层模型将被提交到一个历史拟合过程中,以此来改进数据拟合度或者考虑新收集到的数据。我们关注的是先前建立的相储层模型。虽然我们对模型模拟的方式一无所知,但是我们可以确定一系列随机数,再用多点统计模拟方法来建造一个和现有储层模型十分接近的实现。然后运行一种新的历史拟合程序来更新现有的储层模型,使其拟合两口新生产井的流量数据。 相似文献
4.
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
5.
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
6.
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
7.
Hamidreza Hamdi Ivo Couckuyt Mario Costa Sousa Tom Dhaene 《Computational Geosciences》2017,21(2):267-287
The process of reservoir history-matching is a costly task. Many available history-matching algorithms either fail to perform such a task or they require a large number of simulation runs. To overcome such struggles, we apply the Gaussian Process (GP) modeling technique to approximate the costly objective functions and to expedite finding the global optima. A GP model is a proxy, which is employed to model the input-output relationships by assuming a multi-Gaussian distribution on the output values. An infill criterion is used in conjunction with a GP model to help sequentially add the samples with potentially lower outputs. The IC fault model is used to compare the efficiency of GP-based optimization method with other typical optimization methods for minimizing the objective function. In this paper, we present the applicability of using a GP modeling approach for reservoir history-matching problems, which is exemplified by numerical analysis of production data from a horizontal multi-stage fractured tight gas condensate well. The results for the case that is studied here show a quick convergence to the lowest objective values in less than 100 simulations for this 20-dimensional problem. This amounts to an almost 10 times faster performance compared to the Differential Evolution (DE) algorithm that is also known to be a powerful optimization technique. The sensitivities are conducted to explain the performance of the GP-based optimization technique with various correlation functions. 相似文献
8.
Application of the EnKF and Localization to Automatic History Matching of Facies Distribution and Production Data 总被引：3，自引：3，他引：0
The performance of the ensemble Kalman filter (EnKF) for continuous updating of facies location and boundaries in a reservoir model based on production and facies data for a 3D synthetic problem is presented. The occurrence of the different facies types is treated as a random process and the initial distribution was obtained by truncating a bi-Gaussian random field. Because facies data are highly non-Gaussian, re-parameterization was necessary in order to use the EnKF algorithm for data assimilation; two Gaussian random fields are updated in lieu of the static facies parameters. The problem of history matching applied to facies is difficult due to (1) constraints to facies observations at wells are occasionally violated when productions data are assimilated; (2) excessive reduction of variance seems to be a bigger problem with facies than with Gaussian random permeability and porosity fields; and (3) the relationship between facies variables and data is so highly non-linear that the final facies field does not always honor early production data well. Consequently three issues are investigated in this work. Is it possible to iteratively enforce facies constraints when updates due to production data have caused them to be violated? Can localization of adjustments be used for facies to prevent collapse of the variance during the data-assimilation period? Is a forecast from the final state better than a forecast from time zero using the final parameter fields?To investigate these issues, a 3D reservoir simulation model is coupled with the EnKF technique for data assimilation. One approach to enforcing the facies constraint is continuous iteration on all available data, which may lead to inconsistent model states, incorrect weighting of the production data and incorrect adjustment of the state vector. A sequential EnKF where the dynamic and static data are assimilated sequentially is presented and this approach seems to have solved the highlighted problems above. When the ensemble size is small compared to the number of independent data, the localized adjustment of the state vector is a very important technique that may be used to mitigate loss of rank in the ensemble. Implementing a distance-based localization of the facies adjustment appears to mitigate the problem of variance deficiency in the ensembles by ensuring that sufficient variability in the ensemble is maintained throughout the data assimilation period. Finally, when data are assimilated without localization, the prediction results appear to be independent of the starting point. When localization is applied, it is better to predict from the start using the final parameter field rather than continue from the final state. 相似文献
9.
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
10.
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
11.
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
12.
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
13.
Dynamic data integration for structural modeling: model screening approach using a distance-based model parameterization 总被引：2，自引：0，他引：2
This paper proposes a novel history-matching method where reservoir structure is inverted from dynamic fluid flow response.
The proposed workflow consists of searching for models that match production history from a large set of prior structural
model realizations. This prior set represents the reservoir structural uncertainty because of interpretation uncertainty on
seismic sections. To make such a search effective, we introduce a parameter space defined with a “similarity distance” for
accommodating this large set of realizations. The inverse solutions are found using a stochastic search method. Realistic
reservoir examples are presented to prove the applicability of the proposed method. 相似文献
14.
One of the major limitations of the classical ensemble Kalman filter (EnKF) is the assumption of a linear relationship between
the state vector and the observed data. Thus, the classical EnKF algorithm can suffer from poor performance when considering
highly non-linear and non-Gaussian likelihood models. In this paper, we have formulated the EnKF based on kernel-shrinkage
regression techniques. This approach makes it possible to handle highly non-linear likelihood models efficiently. Moreover,
a solution to the pre-image problem, essential in previously suggested EnKF schemes based on kernel methods, is not required.
Testing the suggested procedure on a simple, illustrative problem with a non-linear likelihood model, we were able to obtain
good results when the classical EnKF failed. 相似文献
15.
16.
Thomas Romary 《Computational Geosciences》2010,14(2):343-355
In history matching of lithofacies reservoir model, we attempt to find multiple realizations of lithofacies configuration
that are conditional to dynamic data and representative of the model uncertainty space. This problem can be formalized in
the Bayesian framework. Given a truncated Gaussian model as a prior and the dynamic data with its associated measurement error,
we want to sample from the conditional distribution of the facies given the data. A relevant way to generate conditioned realizations
is to use Markov chains Monte Carlo (MCMC). However, the dimensions of the model and the computational cost of each iteration
are two important pitfalls for the use of MCMC. Furthermore, classical MCMC algorithms mix slowly, that is, they will not
explore the whole support of the posterior in the time of the simulation. In this paper, we extend the methodology already
described in a previous work to the problem of history matching of a Gaussian-related lithofacies reservoir model. We first
show how to drastically reduce the dimension of the problem by using a truncated Karhunen-Loève expansion of the Gaussian
random field underlying the lithofacies model. Moreover, we propose an innovative criterion of the choice of the number of
components based on the connexity function. Then, we show how we improve the mixing properties of classical single MCMC, without
increasing the global computational cost, by the use of parallel interacting Markov chains. Applying the dimension reduction
and this innovative sampling method drastically lowers the number of iterations needed to sample efficiently from the posterior.
We show the encouraging results obtained when applying the methodology to a synthetic history-matching case. 相似文献
17.
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
18.
Alexandre A. Emerick 《Computational Geosciences》2018,22(5):1175-1186
This paper reports the results of an investigation on the use of a deterministic analysis scheme combined with the method ensemble smoother with multiple data assimilation (ES-MDA) for the problem of assimilating a large number of correlated data points. This is the typical case when history-matching time-lapse seismic data in petroleum reservoir models. The motivation for the use of the deterministic analysis is twofold. First, it tends to result in a smaller underestimation of the ensemble variance after data assimilation. This is particularly important for problems with a large number of measurements. Second, the deterministic analysis avoids the factorization of a large covariance matrix required in the standard implementation of ES-MDA with the perturbed observations scheme. The deterministic analysis is tested in a synthetic history-matching problem to assimilate production and seismic data. 相似文献
19.
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
20.
The history-matching inverse problem from petroleum engineering is analysed using the Imperial College fault model. This fault model produces a challenging inverse problem and is designed to show some of the problems which can occur whilst performing history-matching calculations on complicated geologies. It is shown that there can be multiple distinct geologies which match the history data. Furthermore, it is shown that the maximum-a-posteriori estimate does not correspond to the true geology in some cases. Both of these statements are corroborated via numerical examples where the parameter spaces are ?, ?3, ?7 and ?13. In addition, it is shown that the number of matches which agree with the data increases with dimension for these examples. It is also shown that the different matches can result in different reservoir management decision which, if incorrectly taken, would incur substantial financial penalties. All of these analyses are performed in a systematic manner, where it is shown that the standard algorithms can give a misleading answer. The history-matching problem is written as a minimisation problem, and it is shown that knowledge of all of the local minima is required. This presents significant computational issues as the resulting objective function is highly nonlinear, expensive to evaluate and multimodal. Previously used algorithms have been proved to be inadequate. Parallel tempering is a method which, if run for long enough, can find all the local minima. However, as the objective is expensive, a number of algorithm modifications had to be used to ensure convergence within a reasonable time. This new information is outlined in the paper. The algorithm as implemented produced results and new insights into this problem which were not suspected before. The results produced by this algorithm for the multimodal history-matching problem are superior to all other results of which we are aware. However, a considered amount of computation time was used within this paper, so this result does not infer that the algorithm cannot be improved upon. This algorithm not only produces good results but can be applied to all other history-matching problems. We have shown that this method provides a robust route of finding multiple local optima/solutions to the inverse problem, which is of considerable benefit to the petroleum industry. Furthermore, it is an entirely parallel algorithm which is becoming computationally feasible for other history-matching problems. 相似文献