Evaluation of Gaussian approximations for data assimilation in reservoir models

The Bayesian framework is the standard approach for data assimilation in reservoir modeling. This framework involves characterizing the posterior distribution of geological parameters in terms of a given prior distribution and data from the reservoir dynamics, together with a forward model connecting the space of geological parameters to the data space. Since the posterior distribution quantifies the uncertainty in the geologic parameters of the reservoir, the characterization of the posterior is fundamental for the optimal management of reservoirs. Unfortunately, due to the large-scale highly nonlinear properties of standard reservoir models, characterizing the posterior is computationally prohibitive. Instead, more affordable ad hoc techniques, based on Gaussian approximations, are often used for characterizing the posterior distribution. Evaluating the performance of those Gaussian approximations is typically conducted by assessing their ability at reproducing the truth within the confidence interval provided by the ad hoc technique under consideration. This has the disadvantage of mixing up the approximation properties of the history matching algorithm employed with the information content of the particular observations used, making it hard to evaluate the effect of the ad hoc approximations alone. In this paper, we avoid this disadvantage by comparing the ad hoc techniques with a fully resolved state-of-the-art probing of the Bayesian posterior distribution. The ad hoc techniques whose performance we assess are based on (1) linearization around the maximum a posteriori estimate, (2) randomized maximum likelihood, and (3) ensemble Kalman filter-type methods. In order to fully resolve the posterior distribution, we implement a state-of-the art Markov chain Monte Carlo (MCMC) method that scales well with respect to the dimension of the parameter space, enabling us to study realistic forward models, in two space dimensions, at a high level of grid refinement. Our implementation of the MCMC method provides the gold standard against which the aforementioned Gaussian approximations are assessed. We present numerical synthetic experiments where we quantify the capability of each of the ad hoc Gaussian approximation in reproducing the mean and the variance of the posterior distribution (characterized via MCMC) associated to a data assimilation problem. Both single-phase and two-phase (oil–water) reservoir models are considered so that fundamental differences in the resulting forward operators are highlighted. The main objective of our controlled experiments was to exhibit the substantial discrepancies of the approximation properties of standard ad hoc Gaussian approximations. Numerical investigations of the type we present here will lead to the greater understanding of the cost-efficient, but ad hoc, Bayesian techniques used for data assimilation in petroleum reservoirs and hence ultimately to improved techniques with more accurate uncertainty quantification.     

Evaluation of complex petroleum reservoirs based on data mining methods

In this study, we introduce the application of data mining to petroleum exploration and development to obtain high-performance predictive models and optimal classifications of geology, reservoirs, reservoir beds, and fluid properties. Data mining is a practical method for finding characteristics of, and inherent laws in massive multi-dimensional data. The data mining method is primarily composed of three loops, which are feature selection, model parameter optimization, and model performance evaluation. The method’s key techniques involve applying genetic algorithms to carry out feature selection and parameter optimization and using repeated cross-validation methods to obtain unbiased estimation of generalization accuracy. The optimal model is finally selected from the various algorithms tested. In this paper, the evaluation of water-flooded layers and the classification of conglomerate reservoirs in Karamay oil field are selected as case studies to analyze comprehensively two important functions in data mining, namely predictive modeling and cluster analysis. For the evaluation of water-flooded layers, six feature subset schemes and five distinct types of data mining methods (decision trees, artificial neural networks, support vector machines, Bayesian networks, and ensemble learning) are analyzed and compared. The results clearly demonstrate that decision trees are superior to the other methods in terms of predictive model accuracy and interpretability. Therefore, a decision tree-based model is selected as the final model for identifying water-flooded layers in the conglomerate reservoir. For the reservoir classification, the reservoir classification standards from four types of clustering algorithms, such as those based on division, level, model, and density, are comparatively analyzed. The results clearly indicate that the clustering derived from applying the standard K-means algorithm, which is based on division, provides the best fit to the geological characteristics of the actual reservoir and the greatest accuracy of reservoir classification. Moreover, the internal measurement parameters of this algorithm, such as compactness, efficiency, and resolution, are all better than those of the other three algorithms. Compared with traditional methods from exploration geophysics, the data mining method has obvious advantages in solving problems involving calculation of reservoir parameters and reservoir classification using different specialized field data. Hence, the effective application of data mining methods can provide better services for petroleum exploration and development.     

A novel methodological approach for land subsidence prediction through data assimilation techniques

Computational Geosciences - Anthropogenic land subsidence can be evaluated and predicted by numerical models, which are often built over deterministic analyses. However, uncertainties and...     

Correction to: A novel methodological approach for land subsidence prediction through data assimilation techniques

Computational Geosciences - A Correction to this paper has been published: https://doi.org/10.1007/s10596-021-10079-6     

湖泊及水库富营养化模型研究综述

以湖泊及水库的富营养化研究的发展为主线,着重介绍了三类富营养化模型,即:单一营养物质负荷模型,浮游植物与营养盐相关模型,生态动力学模型。通过对目前国内外常用富营养化模型的建立思路和应用实例进行概括和描述。对不同模型的优缺点和适用范围进行了分析比较,对水体富营养化研究的最新发展趋势进行了预测和展望,为湖泊水库综合管理提供了有效工具。     

Cross-covariances and localization for EnKF in multiphase flow data assimilation

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.     

地下水位在非饱和水流数据同化中的应用

为理解地下水位观测信息在非饱和水流数据同化中的数据价值,建立了基于地下水位动态观测信息的一维饱和-非饱和水流集合卡尔曼滤波,通过虚拟数值实验检验了地下水位观测信息在非饱和水力参数估计和水分校正中的潜在价值。研究结果表明:在以地下水位为唯一观测数据时,同时更新参数和水头比仅更新水头能更好地校正土壤剖面的水头分布;当多层单个水力参数未知时,地下水位观测可以为参数估计提供有效信息;当多层多个参数未知时,地下水位与多层多个参数之间的复杂关系导致观测信息难以估计出最优的(唯一的)参数值;地下水位可作为辅助信息,与含水量观测等信息联合运用改善参数估计和含水量预测精度。     

油气储层自生伊利石分离提纯及其K-Ar 同位素测年技术研究

油气注入史研究对于指导油气勘探具有非常重要的意义.油气储层自生伊利石K-Ar同位素测年可以为油气注入时间研究提供科学依据.文中对油气储层自生伊利石分离提纯及其K-Ar同位素测年技术进行了系统介绍.碎屑含钾矿物杂质对自生伊利石K-Ar同位素年龄具有非常大的影响,文中对此进行了深入研究,建立了一套完整的数据处理技术并提出了"校正年龄"概念.     

Uncertainty analysis of groundwater model based on data assimilation北大核心CSCD

黑河流域中下游地下水系统受上游冰冻圈融水和降雨的补给,由气候变暖导致的冰冻圈萎缩致使中下游地下水系统的稳定性面临更多的风险。地下水模型是地下水系统稳定性评估的有效手段,但是地下水模型参数往往存在较大的不确定性。为此,本文提出了基于数据同化算法的不确定性分析方法,通过包含观测资料信息减小模型不确定性。采用所提方法分析了(基于MODFLOW构建)黑河流域中游地下水模型中13个参数的不确定性,讨论了算法超参数的影响及其最优取值,分析了地下水模型参数的不确定性。实验结果证明数据同化算法可有效减小地下水模型参数的不确定性,观测资料的种类与数量对参数不确定性的减小起到重要作用;不同地下水模型参数的不确定性不同,地表水与地下水相互作用频繁的区域参数不确定性较大;含水层渗透系数、含水层给水度以及灌溉回流系数对模型输出的地下水位输出影响显著,河床水力传导系数对模型输出的河流流量影响较大。本研究将为地下水研究提供更加可靠的模型方法,为西北内流区地下水哺育的绿洲生态系统稳定可持续研究提供重要支撑。     

An evaluation of various data pre-processing techniques with machine learning models for water level prediction

Natural Hazards - Floods are the most frequent type of natural disaster. It destroys wildlife habitat, damages bridges, railways, roads, properties, and puts millions of people at risk. As such,...     

Assimilation of IRS-P4 (MSMR) meteorological data in the NCMRWF global data assimilation system

Oceansat-1 was successfully launched by India in 1999, with two payloads, namely Multi-frequency Scanning Microwave Radiometer (MSMR) and Ocean Color Monitor (OCM) to study the biological and physical parameters of the ocean. The MSMR sensor is configured as an eight-channel radiometer using four frequencies with dual polarization. The MSMR data at 75 km resolution from the Oceansat-I have been assimilated in the National Centre for Medium Range Weather Forecasting (NCMRWF) data assimilation forecast system. The operational analysis and forecast system at NCMRWF is based on a T80L18 global spectral model and Spectral Statistical Interpolation (SSI) scheme for data analysis. The impact of the MSMR data is seen globally, however it is significant over the oceanic region where conventional data are rare. The dry-nature of the control analyses have been removed by utilizing the MSMR data. Therefore, the total precipitable water data from MSMR has been identified as a very crucial parameter in this study. The impact of surface wind speed from MSMR is to increase easterlies over the tropical Indian Ocean. Shifting of the positions of westerly troughs and ridges in the south Indian Ocean has contributed to reduction of temperature to around 30‡S.     

Efficient methods for computing observation impact in 4D-Var data assimilation

This paper presents a practical computational approach to quantify the effect of individual observations in estimating the state of a system. Such a methodology can be used for pruning redundant measurements and for designing future sensor networks. The mathematical approach is based on computing the sensitivity of the analyzed model states (unconstrained optimization solution) with respect to the data. The computational cost is dominated by the solution of a linear system, whose matrix is the Hessian of the cost function, and is only available in operator form. The right-hand side is the gradient of a scalar cost function that quantifies the forecast error of the numerical model. The use of adjoint models to obtain the necessary first- and second-order derivatives is discussed. We study various strategies to accelerate the computation, including matrix-free iterative solvers, preconditioners, and an in-house multigrid solver. Experiments are conducted on both a small-size shallow-water equations model and on a large-scale numerical weather prediction model, in order to illustrate the capabilities of the new methodology.     

Impact of 3D Var GSI-ENKF hybrid data assimilation system

The hybrid two-way coupled 3DEnsVar assimilation system was tested with the NCMRWF global data assimilation forecasting system. At present, this system consists of T574L64 deterministic model and the grid-point statistical interpolation analysis scheme. In this experiment, the analysis system is modified with a two-way coupling with an 80 member Ensemble Kalman Filter of T254L64 resolution and runs are carried out in parallel to the operational system for the Indian summer monsoon season (June–September) for the year 2015 to study its impact. Both the assimilation systems are based on NCEP GFS system. It is found that hybrid assimilation marginally improved the quality of the forecasts of all variables over the deterministic 3D Var system, in terms of statistical skill scores and also in terms of circulation features. The impact of the hybrid system in prediction of extreme rainfall and cyclone track is discussed.