共查询到20条相似文献，搜索用时 31 毫秒
1.
At various stages of petroleum reservoir development, we encounter a large degree of geological uncertainty under which a rational decision has to be made. In order to identify which parameter or group of parameters significantly affects the output of a decision model, we investigate decision-theoretic sensitivity analysis and its computational issues in this paper. In particular, we employ the so-called expected value of partial perfect information (EVPPI) as a sensitivity index and apply multilevel Monte Carlo (MLMC) methods to efficient estimation of EVPPI. In a recent paper by Giles and Goda, an antithetic MLMC estimator for EVPPI is proposed and its variance analysis is conducted under some assumptions on a decision model. In this paper, for an improvement on the performance of the MLMC estimator, we incorporate randomized quasi-Monte Carlo methods within the inner sampling, which results in an multilevel quasi-Monte Carlo (MLQMC) estimator. We apply both the antithetic MLMC and MLQMC estimators to a simple waterflooding decision problem under uncertainty on absolute permeability and relative permeability curves. Through numerical experiments, we compare the performances of the MLMC and MLQMC estimators and confirm a significant advantage of the MLQMC estimator. 相似文献
2.
This paper presents a novel mass-conservative mixed multiscale method for solving flow equations in heterogeneous porous media. The media properties (the permeability) contain multiple scales and high contrast. The proposed method solves the flow equation in a mixed formulation on a coarse grid by constructing multiscale basis functions. The resulting velocity field is mass-conservative on the fine grid. Our main goal is to obtain first-order convergence in terms of the mesh size which is independent of local contrast. This is achieved, first, by constructing some auxiliary spaces, which contain global information that cannot be localized, in general. This is built on our previous work on the generalized multiscale finite element method (GMsFEM). In the auxiliary space, multiscale basis functions corresponding to small (contrast-dependent) eigenvalues are selected. These basis functions represent the high-conductivity channels (which connect the boundaries of a coarse block). Next, we solve local problems to construct multiscale basis functions for the velocity field. These local problems are formulated in the oversampled domain, taking into account some constraints with respect to auxiliary spaces. The latter allows fast spatial decay of local solutions and, thus, allows taking smaller oversampled regions. The number of basis functions depends on small eigenvalues of the local spectral problems. Moreover, multiscale pressure basis functions are needed in constructing the velocity space. Our multiscale spaces have a minimal dimension, which is needed to avoid contrast dependence in the convergence. The method’s convergence requires an oversampling of several layers. We present an analysis of our approach. Our numerical results confirm that the convergence rate is first order with respect to the mesh size and independent of the contrast. 相似文献
3.
《Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards》2013,7(3-4):195-206
A recently developed Bayesian Monte Carlo (BMC) method and its application to safety assessment of structures are described in this paper. We use a one-dimensional BMC method that was proposed in 2009 by Rajabalinejad in order to develop a weighted logical dependence between successive Monte Carlo simulations. Our main objective in this research is to show that the extended BMC can dramatically improve simulation efficiency by using prior information from modelling and outcomes of preceding simulations. We provide theory and numerical algorithms for an extended BMC method for multi-dimensional problems, integrate it with a probabilistic finite element model and apply these coupled models to assessment of reliability of a flood defence for the 17th Street Flood Wall system in New Orleans. This is the first successful demonstration of the BMC method to a complex system. We provide a comparison of the numerical efficiency for the BMC, Monte Carlo (MC) and Dynamic Bounds methods that are used in reliability assessment of complex infrastructures. 相似文献
4.
《Chemical Geology》2006,225(3-4):176-188
We discuss how two techniques, based on (1) lattice dynamics (lattice statics) simulations and (2) Monte Carlo methods may be used to calculate the thermodynamic properties of solid solutions and highly disordered systems. The lattice dynamics calculations involve a full free-energy structural optimisation of each of a number of configurations, followed by thermodynamic averaging. The Monte Carlo simulations include the explicit interchange of cations and use the semi-grand canonical ensemble for chemical potential differences. Both methods are readily applied to high pressures and elevated temperatures without the need for any new parameterisation. We discuss the application of the Monte Carlo technique to the study of surfaces. A range of examples, including binary oxides, spinels, carbonates and surface segregation, is used to illustrate the methods. 相似文献
5.
Jinsong Huang Gordon Fenton D. V. Griffiths Dianqinq Li Chuangbing Zhou 《Landslides》2017,14(2):491-498
The random finite element method (RFEM) combines the random field theory and finite element method in the framework of Monte Carlo simulation. It has been applied to a wide range of geotechnical problems such as slope stability, bearing capacity and the consolidation of soft soils. When the RFEM was first developed, direct Monte Carlo simulation was used. If the probability of failure (p f ) is small, the direct Monte Carlo simulation requires a large number of simulations. Subset simulation is one of most efficient variance reduction techniques for the simulation of small p f . It has been recently proposed to use subset simulation instead of direct Monte Carlo simulation in RFEM. It is noted, however, that subset simulation requires calculation of the factor of safety (FS), while direct Monte Carlo requires only the examination of failure or non-failure. The search for the FS in RFEM could be a tedious task. For example, the search for the FS of slope stability by the strength reduction method (SRM) usually requires much more computational time than a failure or non-failure checking. In this paper, the subset simulation is combined with RFEM, but the need for the search of FS is eliminated. The value of yield function in an elastoplastic finite element analysis is used to measure the safety margin instead of the FS. Numerical experiments show that the proposed approach gives the same level of accuracy as the traditional subset simulation based on FS, but the computational time is significantly reduced. Although only examples of slope stability are given, the proposed approach will generally work for other types of geotechnical applications. 相似文献
6.
We present a variational multiscale mixed finite element method for the solution of Darcy flow in porous media, in which both
the permeability field and the source term display a multiscale character. The formulation is based on a multiscale split
of the solution into coarse and subgrid scales. This decomposition is invoked in a variational setting that leads to a rigorous
definition of a (global) coarse problem and a set of (local) subgrid problems. One of the key issues for the success of the
method is the proper definition of the boundary conditions for the localization of the subgrid problems. We identify a weak
compatibility condition that allows for subgrid communication across element interfaces, a feature that turns out to be essential
for obtaining high-quality solutions. We also remove the singularities due to concentrated sources from the coarse-scale problem
by introducing additional multiscale basis functions, based on a decomposition of fine-scale source terms into coarse and
deviatoric components. The method is locally conservative and employs a low-order approximation of pressure and velocity at
both scales. We illustrate the performance of the method on several synthetic cases and conclude that the method is able to
capture the global and local flow patterns accurately. 相似文献
7.
Reliability analysis of serviceability performance for an underground cavern using a non-intrusive stochastic method 总被引：1，自引：0，他引：1
Dian-Qing Li Shui-Hua Jiang Yi-Feng Chen Chuang-Bing Zhou 《Environmental Earth Sciences》2014,71(3):1169-1182
This paper proposes a non-intrusive stochastic analysis procedure for reliability analysis of the serviceability performance of an underground cavern with an implicit limit state function. This procedure is formulated on the basis of the stochastic response surface method (SRSM) and the deterministic finite element method. First, the SRSM is briefly introduced and implemented through a MATLAB code. Then, the software SIGMA/W is used to perform a deterministic finite element analysis. Next, a link between the MATLAB code and SIGMA/W is developed to automatically pass exchange data between the two platforms. Finally, two examples are presented to illustrate the capacity and validity of the proposed procedure. In the first example, a closed-form limit state function is adopted to validate the SRSM by comparing it with the results obtained from a direct Monte Carlo simulation. In the second example, the serviceability performance of an underground cavern is analyzed to illustrate the capacity of the proposed procedure to handle a reliability problem with an implicit limit state function. The proposed procedure does not require the user to modify the existing deterministic finite element code. The deterministic finite element analysis and the probabilistic analysis are decoupled. This is a major practical advantage because realistic probabilistic analyses are made possible. The SRSM can produce sufficiently accurate reliability results. Furthermore, the method is much more efficient than the direct Monte Carlo simulation. Sensitivity analyses show the effect of the variability of input random variables and the correlation between them on: (1) the probability density functions, (2) the first four order statistical moments, and (3) the probability of failure, which is investigated and discussed. 相似文献
8.
多尺度有限单元法求解非均质多孔介质中的三维地下水流问题 总被引：7，自引：0，他引：7
应用多尺度有限单元法模拟非均质多孔介质中的三维地下水流问题。与传统有限单元法相比，多尺度有限单元法的基函数具有能反映单元内参数变化的优点，所以这种方法能在大尺度上抓住解的小尺度特征获得较精确的解。在介绍多尺度有限单元法求解非均质多孔介质中三维地下水流问题的基本原理之后，对参数水平方向渐变垂直方向突变的非均质多孔介质中的三维地下水流和Borden实验场的三维地下水流分别用多尺度有限单元法和传统等参有限单元法进行了计算，结果表明在模拟高度非均质多孔介质中的三维地下水流问题时，多尺度有限单元法比传统有限单元法有效，既节省计算量又有较高的精度；在模拟非均质性弱的多孔介质中的三维地下水流问题时，多尺度有限单元法虽然也能在大尺度上获得较为精确的解，但效果不明显。 相似文献
9.
In this paper, we study on a history matching approach that consists of finding stable approximations to the problem of minimizing the weighted least-squares functional that penalizes the misfit between the reservoir model predictions G(u) and noisy observations y η . In other words, we are interested in computing an approximation to the minimizer of $\frac {1}{2}\vert \vert \Gamma ^{-1/2}(y^{\eta }-G(u))\vert \vert _{Y}^{2} $ where Γ is the measurements error covariance, Y is the observation space, and X is a set of admissible parameters. This is an ill-posed nonlinear inverse problem that we address by means of the regularizing Levenberg–Marquardt scheme developed by Hanke (Inverse Probl. 13:79–95, 1997; J. Integr. Equ. Appl. 22(2):259–283, 2010). Under certain conditions on G, the theory of Hanke (Inverse Probl. 13:79–95, 1997; J. Integr. Equ. Appl. 22(2):259–283, 2010) ensures the convergence of the scheme to stable approximations to the inverse problem. We propose an implementation of the regularizing Levenberg–Marquardt scheme that enforces prior knowledge on the geologic properties. In particular, the prior mean $\overline {u}$ is incorporated in the initial guess of the algorithm, and the prior error covariance C is enforced through the definition of the parameter space X. Our main goal is to numerically show that the proposed implementation of the regularizing Levenberg–Marquardt scheme of Hanke is a robust method capable of providing accurate estimates of the geologic properties for small noise measurements. In addition, we provide numerical evidence of the convergence and regularizing results predicted by the theory of Hanke (Inverse Probl. 13:79–95, 1997; J. Integr. Equ. Appl. 22(2):259–283, 2010) for a prototypical oil–water reservoir model. The performance for recovering the true permeability with the regularizing Levenberg–Marquardt scheme is compared to the typical approach of computing the maximum a posteriori (MAP) estimator. In particular, we compare the proposed application of the regularizing Levenberg–Marquardt (LM) scheme against the standard LM approach of Li et al. (SPE J. 8(4):328–340, 2003) and Reynolds et al. (2008) for computing the MAP. Our numerical experiments suggest that the history matching approach based on iterative regularization is robust and could potentially be used to improve further on various methodologies already proposed as effective tools for history matching in petroleum reservoirs. 相似文献
10.
Dislocation modelling of an earthquake fault is of great importance due to the fact that ground surface response may be predicted by the model. However, geological features of a fault cannot be measured exactly, and therefore these features and data involve uncertainties. This paper presents a Monte Carlo based random model of faults with finite element method incorporating split node technique to impose the effects of discontinuities. Length and orientation of the fault are selected as random parameters in the domain model, and hence geometrical uncertainties are encountered. Mean and standard deviation values, as well as probability density function of ground surface responses due to the dislocation are computed. Based on analytical and numerical calculation of dislocation, two approaches of Monte Carlo simulations are proposed. Various comparisons are examined to illustrate the capability of both methods for random simulation of faults. 相似文献
11.
12.
In this paper, The Monte Carlo method is incorporated into the finite element method (FEM) to conduct seepage analysis with a free surface. For the transitional element cut by the free surface, it is used to calculate the composite permeability coefficient, as well as to perform the integration directly using Monte Carlo integration. This new algorithm requires less iteration procedures for convergence. The convergence of the method is also proved for cases where there is a significant difference between the permeability coefficient above and below the free surface. 相似文献
13.
This paper presents a second-order work analysis in application to geotechnical problems by using a novel effective multiscale approach. To abandon complicated equations involved in conventional phenomenological models, this multiscale approach employs a micromechanically-based formulation, in which only four parameters are involved. The multiscale approach makes it possible a coupling of the finite element method (FEM) and the micromechanically-based model. The FEM is used to solve the boundary value problem (BVP) while the micromechanically-based model is utilized at the Gauss point of the FEM. Then, the multiscale approach is used to simulate a three-dimensional triaxial test and a plain-strain footing. On the basis of the simulations, material instabilities are analyzed at both mesoscale and global scale. The second-order work criterion is then used to analyze the numerical results. It opens a road to interpret and understand the micromechanisms hiding behind the occurrence of failure in geotechnical issues. 相似文献
14.
For analyzing low probability slope failures, a modified version of subset simulation, based on performance-based subset selection rather than the usual probability-based subset selection, is combined with the random finite element method. The application to an idealized slope is used to study the efficiency and consistency of the proposed method compared to classical Monte Carlo simulations and the shear strength reduction (SSR) method. Results demonstrate that failure events taking place without strength reduction have different modes of failure than stable slopes brought to failure by SSR. The correlation between sliding volume and factor of safety is also demonstrated. 相似文献
15.
Multiscale mixed/mimetic methods on corner-point grids 总被引：1，自引：0，他引：1
Multiscale simulation is a promising approach to facilitate direct simulation of large and complex grid models for highly
heterogeneous petroleum reservoirs. Unlike traditional simulation, approaches based on upscaling/downscaling, multiscale methods
seek to solve the full flow problem by incorporating subscale heterogeneities into local discrete approximation spaces. We
consider a multiscale formulation based on a hierarchical grid approach, where basis functions with subgrid resolution are
computed numerically to correctly and accurately account for subscale variations from an underlying (fine-scale) geomodel
when solving the global flow equations on a coarse grid. By using multiscale basis functions to discretise the global flow
equations on a (moderately sized) coarse grid, one can retain the efficiency of an upscaling method and, at the same time,
produce detailed and conservative velocity fields on the underlying fine grid. For pressure equations, the multiscale mixed
finite-element method (MsMFEM) has been shown to be a particularly versatile approach. In this paper, we extend the method
to corner-point grids, which is the industry standard for modelling complex reservoir geology. To implement MsMFEM, one needs
a discretisation method for solving local flow problems on the underlying fine grids. In principle, any stable and conservative
method can be used. Here, we use a mimetic discretisation, which is a generalisation of mixed finite elements that gives a
discrete inner product, allows for polyhedral elements, and can (easily) be extended to curved grid faces. The coarse grid
can, in principle, be any partition of the subgrid, where each coarse block is a connected collection of subgrid cells. However,
we argue that, when generating coarse grids, one should follow certain simple guidelines to achieve improved accuracy. We
discuss partitioning in both index space and physical space and suggest simple processing techniques. The versatility and
accuracy of the new multiscale mixed methodology is demonstrated on two corner-point models: a small Y-shaped sector model
and a complex model of a layered sedimentary bed. A variety of coarse grids, both violating and obeying the above mentioned
guidelines, are employed. The MsMFEM solutions are compared with a reference solution obtained by direct simulation on the
subgrid. 相似文献
16.
This work presents the application of a Monte Carlo simulation method to perform an statistical analysis of transient variably saturated flow in an hypothetical random porous media. For each realization of the stochastic soil parameters entering as coefficients in Richards' flow equation, the pressure head and the flow field are computed using a mixed finite element procedure for the spatial discretization combined with a backward Euler and a modified Picard iteration in time. The hybridization of the mixed method provides a novel way for evaluating hydraulic conductivity on interelement boundaries. The proposed methodology can handle both large variability and fractal structure in the hydraulic parameters. The saturated conductivity K
s and the shape parameter vg in the van Genuchten model are treated as stochastic fractal functions known as fractional Brownian motion (fBm) or fractional Gaussian noise (fGn). The statistical moments of the pressure head, water content, and flow components are obtained by averaging realizations of the fractal parameters in Monte Carlo fashion. A numerical example showing the application of the proposed methodology to characterize groundwater flow in highly heterogeneous soils is presented. 相似文献
17.
Monte Carlo模拟法与基坑变形的可靠度分析 总被引：4，自引：0，他引：4
将Ｍｏｎｔｅ Ｃａｒｌｏ模拟法与有限元技术结合,对基坑变形的稳定怀进行了可靠度分析,并通过重构响应面来提高Ｍｏｎｔｅ Ｃａｒｌｏ模拟法的计算效率,研究表明该方法可行,计算结果较符合实际。 相似文献
18.
The reliability of heterogeneous slopes can be evaluated using a wide range of available probabilistic methods. One of these methods is the random finite element method (RFEM), which combines random field theory with the non‐linear elasto‐plastic finite element slope stability analysis method. The RFEM computes the probability of failure of a slope using the Monte Carlo simulation process. The major drawback of this approach is the intensive computational time required, mainly due to the finite element analysis and the Monte Carlo simulation process. Therefore, a simplified model or solution, which can bypass the computationally intensive and time‐consuming numerical analyses, is desirable. The present study investigates the feasibility of using artificial neural networks (ANNs) to develop such a simplified model. ANNs are well known for their strong capability in mapping the input and output relationship of complex non‐linear systems. The RFEM is used to generate possible solutions and to establish a large database that is used to develop and verify the ANN model. In this paper, multi‐layer perceptrons, which are trained with the back‐propagation algorithm, are used. The results of various performance measures indicate that the developed ANN model has a high degree of accuracy in predicting the reliability of heterogeneous slopes. The developed ANN model is then transformed into relatively simple formulae for direct application in practice. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
19.
The present paper proposes a new family of multiscale finite volume methods. These methods usually deal with a dual mesh resolution, where the pressure field is solved on a coarse mesh, while the saturation fields, which may have discontinuities, are solved on a finer reservoir grid, on which petrophysical heterogeneities are defined. Unfortunately, the efficiency of dual mesh methods is strongly related to the definition of up-gridding and down-gridding steps, allowing defining accurately pressure and saturation fields on both fine and coarse meshes and the ability of the approach to be parallelized. In the new dual mesh formulation we developed, the pressure is solved on a coarse grid using a new hybrid formulation of the parabolic problem. This type of multiscale method for pressure equation called multiscale hybrid-mixed method (MHMM) has been recently proposed for finite elements and mixed-finite element approach (Harder et al. 2013). We extend here the MH-mixed method to a finite volume discretization, in order to deal with large multiphase reservoir models. The pressure solution is obtained by solving a hybrid form of the pressure problem on the coarse mesh, for which unknowns are fluxes defined on the coarse mesh faces. Basis flux functions are defined through the resolution of a local finite volume problem, which accounts for local heterogeneity, whereas pressure continuity between cells is weakly imposed through flux basis functions, regarded as Lagrange multipliers. Such an approach is conservative both on the coarse and local scales and can be easily parallelized, which is an advantage compared to other existing finite volume multiscale approaches. It has also a high flexibility to refine the coarse discretization just by refinement of the lagrange multiplier space defined on the coarse faces without changing nor the coarse nor the fine meshes. This refinement can also be done adaptively w.r.t. a posteriori error estimators. The method is applied to single phase (well-testing) and multiphase flow in heterogeneous porous media. 相似文献
20.
This paper deals with slope reliability analysis incorporating two-dimensional spatial variation. Two methods, namely the method of autocorrelated slices and the method of interpolated autocorrelations, are proposed for this purpose. Investigations are carried out based on the limit equilibrium method of slices. First-order-reliability-method (FORM) is coupled with deterministic slope stability analysis using the constrained optimization approach. Systematic search for the probabilistic critical slip surface has been carried out in this study. It is shown that both methods work well in modeling 2-D spatial variation. The results of slope reliability analysis are validated by Monte Carlo simulations. Failure probabilities obtained by FORM agree well with simulation results. It is found that 2-D spatial variation significantly influences the reliability analysis, and that the reliability index is more sensitive to vertical autocorrelation distance than to horizontal autocorrelation distance. Based on this study, failure probability is found significantly overestimated when spatial variation is ignored. Finally, the possible use of the method of interpolated autocorrelations in a probabilistic finite element analysis is suggested. 相似文献