An enhanced ensemble Kalman filter scheme incorporating model error in sequential coupling between flow and geomechanics

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.     

Performance of the ensemble Kalman filter outside of existing wells for a channelized reservoir

The ensemble Kalman filter (EnKF) appears to give good results for matching production data at existing wells. However, the predictive power of these models outside of the existing wells is much more uncertain. In this paper, for a channelized reservoir for five different cases with different levels of information the production history is matched using the EnKF. The predictive power of the resulting model is tested for the existing wells and for new wells. The results show a consistent improvement for the predictions at the existing wells after assimilation of the production data, but not for prediction of production at new well locations. The latter depended on the settings of the problem and prior information used. The results also showed that the fit during the history match was not always a good predictor for predictive capabilities of the history match model. This suggests that some form of validation outside of observed wells is essential.     

Combining sensitivities and prior information for covariance localization in the ensemble Kalman filter for petroleum reservoir applications

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.     

Non-parametric Bayesian networks for parameter estimation in reservoir simulation: a graphical take on the ensemble Kalman filter (part I)

Reservoir simulation models are used both in the development of new fields and in developed fields where production forecasts are needed for investment decisions. When simulating a reservoir, one must account for the physical and chemical processes taking place in the subsurface. Rock and fluid properties are crucial when describing the flow in porous media. In this paper, the authors are concerned with estimating the permeability field of a reservoir. The problem of estimating model parameters such as permeability is often referred to as a history-matching problem in reservoir engineering. Currently, one of the most widely used methodologies which address the history-matching problem is the ensemble Kalman filter (EnKF). EnKF is a Monte Carlo implementation of the Bayesian update problem. Nevertheless, the EnKF methodology has certain limitations that encourage the search for an alternative method.For this reason, a new approach based on graphical models is proposed and studied. In particular, the graphical model chosen for this purpose is a dynamic non-parametric Bayesian network (NPBN). This is the first attempt to approach a history-matching problem in reservoir simulation using a NPBN-based method. A two-phase, two-dimensional flow model was implemented for a synthetic reservoir simulation exercise, and initial results are shown. The methods’ performances are evaluated and compared. This paper features a completely novel approach to history matching and constitutes only the first part (part I) of a more detailed investigation. For these reasons (novelty and incompleteness), many questions are left open and a number of recommendations are formulated, to be investigated in part II of the same paper.     

A simple Monte Carlo method for estimating the chance of a cyclone impact

Natural Hazards - Cyclones endanger life and cause great financial impact on interior and coastal regions through the destruction of buildings and land. Governments need to have a way of estimating...     

A Simple Monte Carlo Method for Locating the Three-dimensional Critical Slip Surface of a Slope

Based on the assumption of the plain-strain problem, various optimization or random search methods have been developed for locating the critical slip surfaces in slope-stability analysis, but none of such methods is applicable to the 3D case. In this paper, a simple Monte Carlo random simulation method is proposed to identify the 3D critical slip surface. Assuming the initial slip to be the lower part of a slip ellipsoid, the 3D critical slip surface is located by means of a minimized 3D safety factor. A column-based 3D slope stability analysis model is used to calculate this factor. In this study, some practical cases of known minimum safety factors and critical slip surfaces in 2D analysis are extended to 3D slope problems to locate the critical slip surfaces. Compared with the 2D result, the resulting 3D critical slip surface has no apparent difference in terms of only cross section, but the associated 3D safety factor is definitely higher.     

多尺度非均质多孔介质中溶质运移的蒙特卡罗模拟

探讨了将蒙特卡罗(Monte Carlo)方法应用于多尺度非均质含水层中溶质运移模拟的方法。所研究的含水层由两种具有不同渗透系数统计特征的多孔介质所组成,每一种多孔介质是非均质的,且其渗透系数场符合平稳假设,而整个模拟区的渗透系数是非平稳的。Monte Carlo方法要求参数是平稳的,因此,分别对两种多孔介质产生若干随机渗透系数场后,用两种方法进行组合,并进行溶质运移的模拟计算。通过对计算结果的分析,综合考虑计算精度、计算时间等因素,得出了处理多尺度非均质多孔介质中溶质运移问题的较好方法。     

Revelation of nuclear tracks and dislocations: A Monte Carlo simulation of mineral etching

A simple atomistic Monte Carlo simulation suggests that there are up to four stages in the evolution of an etch pit in the (0 0 1)-surface of an idealised regular lattice. During the first stage, the etch pit is an inverted pyramid; its horizontal and vertical dimensions increase at a constant rate; the apparent horizontal (v_h) and vertical (v_d) growth rates are faster than during all subsequent stages but nevertheless less than the step retreat rate (v_s) on account of surface etching (v_v). The pyramid apex is truncated in the second stage; it is thereafter bounded by an expanding bottom plane and shrinking lateral walls; this is accompanied by a gradual decrease of v_h; v_d drops to a negative value indicating a slow decrease of the etch-pit depth; the bottom plane acquires a concave-up curvature; the outward curvature of the walls, initiated during the first stage, increases. During the third stage the etch pit consists of a single concave-up bottom plane; v_h and v_d decrease at declining rates; consecutive etch-pit profiles are scalable in the horizontal direction. The hypothetical fourth stage is inferred but not documented by the simulations; it sets in when v_h is reduced to zero; unless this corresponds to an as yet unidentified steady-state condition, the etch pit from here on forth shrinks until it eventually disappears altogether. The sole cause for this succession is the process of stochastic rounding of confined steps and faces.The triangular footprint of recoil-track, fission-track, ion-track and dislocation etch pits in trioctahedral mica and its compliance with the monoclinic symmetries implies that the relevant periodic bond chains are O-Mg/Fe-O chains in the octahedral layer. The size distribution of etched recoil tracks is due to (1) depth variations resulting from the size distribution of the latent tracks, (2) the random truncation of the surface tracks, (3) the variable rate of etch-pit enlargement and (4) the fact that new tracks are exposed at the surface due to surface etching. The greater size of dislocation, fission-track and ion-track etch pits is due to their greater extent below the surface. The increase of the number of etched tracks with etching time due to bulk etching is non-linear because the bulk etch rate v_v is not constant. The evolution of etch-pit shape with continued etching can also cause loss of tracks due to observation effects related to loss of contrast.     

The inclusive and simplified forms of Bayesian interpolation for general and monotonic models using Gaussian and Generalized Beta distributions with application to Monte Carlo simulations

A recently developed Bayesian interpolation method (BI) and its application to safety assessment of a flood defense structure are described in this paper. We use a one-dimensional Bayesian Monte Carlo method (BMC) that has been proposed in (Rajabalinejad 2009) to develop a weighted logical dependence between neighboring points. The concept of global uncertainty is adequately explained and different uncertainty association models (UAMs) are presented for linking the local and global uncertainty. Based on the global uncertainty, a simplified approach is introduced. By applying the global uncertainty, we apply the Guassian error estimation to general models and the Generalized Beta (GB) distribution to monotonic models. Our main objective in this research is to simplify the newly developed BMC method and demonstrate that it can dramatically improve the simulation efficiency by using prior information from outcomes of the preceding simulations. We provide theory and numerical algorithms for the BI method geared to multi-dimensional problems, integrate it with a probabilistic finite element model, and apply the coupled models to the reliability assessment of a flood defense for the 17th Street Flood Wall system in New Orleans.     

Crossover of cation partitioning in olivines: a combination of ab initio and Monte Carlo study

We report studies based on a combination of ab initio electronic structure and Monte Carlo (MC) technique on the problem of cation partitioning among inequivalent octahedral sites, M1 and M2 in mixed olivines containing Mg²⁺ and Fe²⁺ ions. Our MC scheme uses interactions derived out of ab initio, density functional calculations carried out on measured crystal structure data. Our results show that there is no reversal of the preference of Fe for M1 over M2 as a function of temperature. Our findings do not agree with the experimental findings of Redfern et al. (Phys Chem Miner 27:630–637, 2000), but are in agreement with those of Heinemann et al. (Eur J Mineral 18:673–689, 2006) and Morozov et al. (Eur J Mineral 17:495–500, 2005).     

A comparison of ecosystem dynamics in freshwater wetlands

The effects of system closure on the dynamics of productivity and nutrient cycling are examined in four wetlands that differ in plant growth form and magnitudes and sources of water input and nutrient loading. Dynamics in relatively closed ombrotrophicCarex marsh andTaxodium swamp systems from Okefenokee Swamp are compared to those in open, rheotrophic riparian systems. The riparian systems examined includeZizaniopsis marshes along the tidal freshwater portion of the Altamaha River in Georgia and a matureTaxodium-Nyssa swamp along the Cache River in Illinois. Water budgets in the ombrotrophic systems are dominated by precipitation inputs while in the riparian wetlands they are dominated by overbank flooding. Nutrient loading to the open and closed systems differs by only two orders of magnitude, the former depending on atmospheric inputs and the latter depending on tidal and riverine inputs. Comparisons of nutrient import, export, and retention indicate that greater than 90% of inorganic nutrients are retained in the closed systems while less than 5% are retained in the open systems. Nutrient budgets for wetland vegetation, including aboveground uptake, root uptake, leaching, death, and translocation, are constructed. Strong differences in nutrient conservation within plant communities are found between marsh and forested closed systems and between open and closed systems as a whole. There is the indication that nutrients turn over more rapidly and nutrient cycles are less retentive and conservative as systems become more open and nutrient inputs increase. Nutrients turn over more rapidly in marshes with nonwoody vegetation than in swamp forests. This phenomena is partially attributable to the growth form of the vegetation as trees store vast amounts of high Canutrient ratio biomass in boles. Substituting space for time and marsh and swamp wetlands for young and mature ecosystems enables patterns of productivity and nutrient cycling for these wetlands to be compared with Odum’s (1969) predictions of ecosystem development. Patterns of ecosystem development in wetlands agree with those predicted for terrestrial systems in general, but there are many areas of contradiction. The degree of system closure appears to be a major factor controlling nutrient retention and cycling in wetland ecosystems. System closure is also likely to be important in determining the response of wetland systems to global increases in CO₂ levels.     

A review of Markov Chain Monte Carlo and information theory tools for inverse problems in subsurface flow

Parameter identification is one of the key elements in the construction of models in geosciences. However, inherent difficulties such as the instability of ill-posed problems or the presence of multiple local optima may impede the execution of this task. Regularization methods and Bayesian formulations, such as the maximum a posteriori estimation approach, have been used to overcome those complications. Nevertheless, in some instances, a more in-depth analysis of the inverse problem is advisable before obtaining estimates of the optimal parameters. The Markov Chain Monte Carlo (MCMC) methods used in Bayesian inference have been applied in the last 10 years in several fields of geosciences such as hydrology, geophysics or reservoir engineering. In the present paper, a compilation of basic tools for inference and a case study illustrating the practical application of them are given. Firstly, an introduction to the Bayesian approach to the inverse problem is provided together with the most common sampling algorithms with MCMC chains. Secondly, a series of estimators for quantities of interest, such as the marginal densities or the normalization constant of the posterior distribution of the parameters, are reviewed. Those reduce the computational cost significantly, using only the time needed to obtain a sample of the posterior probability density function. The use of the information theory principles for the experimental design and for the ill-posedness diagnosis is also introduced. Finally, a case study based on a highly instrumented well test found in the literature is presented. The results obtained are compared with the ones computed by the maximum likelihood estimation approach.     

Field application at a DNAPL-contaminated site in Nanjing and discussion of a source search algorithm based on stochastic modeling and Kalman filter

Delineation of contaminant sources is vital for successful groundwater and soil remediation. With reliable source information, remediation time and cost can be dramatically reduced. An optimal contamination source search strategy incorporating Monte Carlo method, Kalman filtering and fuzzy set theory was applied to a contaminated site in Nanjing to define suspected multiple DNAPL source locations. Using the available nine sample data, the algorithm identified sources #1 and #4 as true sources, and sources #5 and #6 as false ones. The algorithm results for sources #2 and #3 were inconclusive. Three numerical experiments based on specific site conditions were then designed and conducted to determine the influencing factors on the algorithm’s convergence in sources #2 and #3. The numerical experiments tested the effect of multiple sources, the effect of the sources location in relation to the groundwater flow direction and the effect of a low permeability field on the convergence of the algorithm. Based on the numerical experiments and an understanding of the manufacturing site operations, sources #2 and #3 are likely to be true sources. Their moderate weights have been stabilized due to the existence of multiple true sources and the scarcity of informative sampling data, caused by the low permeability field. The moderate weight value of source #3 also includes a contribution from an overlapping plume caused by the sources’ parallel-to-flow layout pattern. It can be concluded that the algorithm works best for high permeability sites where potential source locations are scattered and source location patterns are orthogonal to the groundwater flow.     

A seismicity revision and a probabilistic seismic hazard assessment using the Monte Carlo approach for the Canary Islands (Spain)

Natural Hazards - This study consists of a seismicity revision and the assessment of the probabilistic seismic hazard of the Canary Islands. In order to analyze its seismotectonics and associated...     

Monte Carlo simulations of the dissolution of borosilicate and aluminoborosilicate glasses in dilute aqueous solutions

The aim of this study was to use Monte Carlo simulations to provide atomic-level insights into the dissolution behavior of borosilicate and aluminoborosilicate glasses in dilute aqueous solutions. In the first part of this work, the effects of different structural features, such as the presence of non-bridging oxygens (NBO) or the formation of boroxol rings, on glass dissolution were evaluated separately and led to the following conclusions. (1) The dependence of the dissolution rate on the amount of NBO was found to be linear at all Si/B ratios and the accelerating effect of NBO was shown to increase with increasing Si/B ratio. (2) The formation of boroxol rings and of clusters of boroxol rings resulted in an increase of the dissolution rate at all Si/B ratios and, again, the extent of the rate increase was strongly dependent on the Si/B ratio. (3) For aluminosilicate glasses, the implementation of the aluminum avoidance rule was found to increase the rate of dissolution relative to that obtained for a random distribution.In the second part of this work, the dissolution of the NeB glasses studied by Pierce et al. (2010) was modeled in dilute aqueous solutions. Pierce et al. concluded from their study that either the rupture of the Al-O bonds or that of the Si-O bonds was the rate-limiting step controlling the dissolution of the NeB glasses. The simulations refined this conclusion and showed that, at low B/Al ratios, the rupture of both Al-O-Si and Si-O-Si linkages contributed to the dissolution rate whereas, at high B/Al ratios, the dissolution rate was independent of the rupture of Al-O-Si linkages and was controlled by S¹ sites (silicon sites at the glass-water interface with one connection to nearest-neighbor sites) and dissolution via detachment of clusters.     

A comparison of linear and nonlinear models for open-circuit ball mill grinding

A detailed comparison is made of the capability of population balance models to predict steady-state product size distributions of a pilot-scale ball mill. The mill was operated at 60% solids with feed rates of crystalline limestone ranging from 90 to 450 kg/hr (200 to 1000 lb/hr). Two types of lumped parameter models are compared: a linear model in which size reduction parameters are independent of size consist and a nonlinear model in which these parameters are dependent on size consist. The nonlinear model is based on an empirical correlation between rate of breakage and size consist in the mill. Results indicate that the nonlinear model gives the most accurate predictions of product size distributions, however, at the cost of significantly more complex computations.     

基于镁铁-超镁铁岩中单斜辉石主量元素含量的决策树集成算法对比

依靠岩浆构造环境的地球化学成分认识岩浆形成过程是岩石地球化学中的重要应用。当前利用岩石地球化学成分判别构造环境的工作还不够深入。用4种基于决策树的机器学习方法对来自全球新生代洋岛玄武岩(OIB)、岛弧玄武岩(IAB)及大洋中脊玄武岩(MORB)等镁铁-超镁铁岩中单斜辉石的13种主量元素构成数据集进行了岩浆构造环境判别和主要特征排序。通过对比4种基于决策树的机器学习方法,验证了树类算法对于地球化学成分识别问题的有效性,并总结出4种方法在处理岩浆构造环境判别问题时的优劣:决策树算法判别过程更易于理解,但是其准确率欠佳;boosting算法中的AdaBoost和GBDT对于岩浆构造环境的鉴别准确度较高,但构造过程复杂;bagging集成算法随机森林在权衡性能和模型可理解性时不失为一个良好的选择。此外,还通过4种算法的特征重要性排序得出Cr_2O_3,TFeO,TiO_2,FeO和Al_2O_3是进行岩浆构造环境判别的重要成分。     

甲玛与世界级铜矿的初步对比及下一步找矿工作建议

西藏甲玛铜多金属矿床随着勘探工作的深入取得重大成果,已成为冈底斯斑岩铜矿带内最重要的大型矿床之一.通过对世界级铜矿含义的解析,与北美、南美、环太平洋西南部及其他主要产区的世界级铜矿进行对比,认为甲玛铜多金属矿床以矽卡岩型、斑岩型和角岩型三位一体、形成于晚第三纪青藏高原隆升阶段为显著特点,具有成为世界级铜、金、银、钼多金...