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In this paper, we describe an efficient approach for quantifying uncertainty in two-phase flow applications due to perturbations of the permeability in a multiscale heterogeneous porous medium. The method is based on the application of the multiscale finite element method within the framework of Monte Carlo simulation and an efficient preprocessing construction of the multiscale basis functions. The quantities of interest for our applications are the Darcy velocity and breakthrough time and we quantify their uncertainty by constructing the respective cumulative distribution functions. For the Darcy velocity we use the multiscale finite element method, but due to lack of conservation, we apply the multiscale finite volume element method as an alternative for use with the two-phase flow problem. We provide a number of numerical examples to illustrate the performance of the method. 相似文献
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Victor Ginting Felipe Pereira Michael Presho Shaochang Wo 《Computational Geosciences》2011,15(4):691-707
In this paper, we develop a procedure for subsurface characterization of a fractured porous medium. The characterization involves
sampling from a representation of a fracture’s permeability that has been suitably adjusted to the dynamic tracer cut measurement
data. We propose to use a type of dual-porosity, dual-permeability model for tracer flow. This model is built into the Markov
chain Monte Carlo (MCMC) method in which the permeability is sampled. The Bayesian statistical framework is used to set the
acceptance criteria of these samples and is enforced through sampling from the posterior distribution of the permeability
fields conditioned to dynamic tracer cut data. In order to get a sample from the distribution, we must solve a series of problems
which requires a fine-scale solution of the dual model. As direct MCMC is a costly method with the possibility of a low acceptance
rate, we introduce a two-stage MCMC alternative which requires a suitable coarse-scale solution method of the dual model.
With this filtering process, we are able to decrease our computational time as well as increase the proposal acceptance rate.
A number of numerical examples are presented to illustrate the performance of the method. 相似文献
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The problem of multiphase phase flow in heterogeneous subsurface porous media is one involving many uncertainties. In particular, the permeability of the medium is an important aspect of the model that is inherently uncertain. Properly quantifying these uncertainties is essential in order to make reliable probabilistic-based predictions and future decisions. In this work, a measure-theoretic framework is employed to quantify uncertainties in a two-phase subsurface flow model in high-contrast media. Given uncertain saturation data from observation wells, the stochastic inverse problem is solved numerically in order to obtain a probability measure on the space of unknown permeability parameters characterizing the two-phase flow. As solving the stochastic inverse problem requires a number of forward model solves, we also incorporate the use of a conservative version of the generalized multiscale finite element method for added efficiency. The parameter-space probability measure is used in order to make predictions of saturation values where measurements are not available, and to validate the effectiveness of the proposed approach in the context of fine and coarse model solves. A number of numerical examples are offered to illustrate the measure-theoretic methodology for solving the stochastic inverse problem using both fine and coarse solution schemes. 相似文献
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Computational Geosciences - In this work, we consider an online enrichment procedure in the context of the Generalized Multiscale Finite Element Method (GMsFEM) for the two-phase flow model in... 相似文献
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