[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

A general form of the double porosity model of single phase flow in a naturally fractured reservoir is derived from homogenization theory. The microscopic model consists of the usual equations describing Darcy flow in a reservoir, except that the porosity and permeability coefficients are highly discontinuous. Over the matrix domain, the coefficients are scaled by a parameter $\epsilon $ representing the size of the matrix blocks. This scaling preserves the physics of the flow in the matrix as $\epsilon $ tends to zero. An effective macroscopic limit model is obtained that includes the usual Darcy equations in the matrix blocks and a similar equation for the fracture system that contains a term representing a source of fluid from the matrix. The convergence is shown by extracting weak limits in appropriate Hilbert spaces. A dilation operator is utilized to see the otherwise vanishing physics in the matrix blocks as $\epsilon $ tends to zero.

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Derivation of the double porosity model of single phase flow via homogenization theory

During the last two decades, the water resources planning and management profession has seen a dramatic increase in the development and application of various types of evolutionary algorithms (EAs). This observation is especially true for application of genetic algorithms, arguably the most popular of the several types of EAs. Generally speaking, EAs repeatedly prove to be flexible and powerful tools in solving an array of complex water resources problems. This paper provides a comprehensive review of state-of-the-art methods and their applications in the field of water resources planning and management. A primary goal in this ASCE Task Committee effort is to identify in an organized fashion some of the seminal contributions of EAs in the areas of water distribution systems, urban drainage and sewer systems, water supply and wastewater treatment, hydrologic and fluvial modeling, groundwater systems, and parameter identification. The paper also identifies major challenges and opportunities for the future, ...

State of the Art for Genetic Algorithms and Beyond in Water Resources Planning and Management

Strong Formulation Finite Element Method Based on Differential Quadrature: A Survey

Representative samples (as defined in section 1.5, chapter 1) from the economic zone of the lower Mn orebody, including the lithostratigraphic zones M, C and N, from eight drill cores in the study area (Fig. 1.4) were selected for whole rock chemical analysis to represent all stages of supergene alteration. Although the X-zone has very good manganese grades, it was not used for modeling purposes, as it is eroded over large parts of the suboutcrop area below the Kalahari Formation and very few drill cores intersect strongly supergene altered X-zone. Among the 8 selected drill cores Rex 16, 44 and 85 represent the geochemistry of unaltered braunite lutite protore, Rex 70, 71 and Rex 74 represent weakly supergene, and Rex 2 and 24 strongly supergene altered braunite lutite (Fig. 4.1). It is important to note that for comparative purposes and mass balance calculations, it was necessary to link supergene altered samples to unaltered reference samples of the same lithostratigraphic zone from different core intersections (Table 4.1). To assure compatibility, unaltered reference samples were selected from drill cores located in close proximity to the altered drill cores to be evaluated. Consequently, samples from REX 16 are reference for REX 2, 24 and 74, and samples from REX 85 are used as reference for REX 70 and 71 (Fig.4.1).

Geochemistry (地球化学・前半)

A mathematically rigorous method of homogenization is presented and used to analyze the equivalent behavior of transient flow of two incompressible fluids through heterogeneous media Asymptotic qpansions and H-convergence lead to the definition of a global or effective model of an equivalent homogeneous reservoir Numerical computations to obtain the homogenized coefficients of the entire reservoir have been carried out via a finite element method Numerical experiments involving the simulation of incompressible two-phase flow have been performed for each heterogeneous medium and for the homogenized medium as well as for other averaging methods The results of the simulations are compared in terms of the transient saturation contours, production curves, and pressure distributions Results obtained from the simulations with the homogenization method presented show good agreement with the heterogeneous simulations

Two-phase flow in heterogeneous porous media

Convergence of finite volume schemes for a degenerate convection-diffusion equation arising in flow in porous media

A mathematically rigorous method of homogenization is presented and used to analyze the equivalent behavior of transient flow of two incompressible fluids through heterogeneous media Asymptotic expansions and H-convergence lead to the definition of a global or effective model of an equivalent homogeneous reservoir Numerical computations to obtain the homogenized coefficients of the entire reservoir have been carried out via a finite element method Numerical experiments involving the simulation of incompressible two-phase flow have been performed for each heterogeneous medium and for the homogenized medium as well as for other averaging methods The results of the simulations are compared in terms of the transient saturation contours, production curves, and pressure distributions Results obtained from the simulations with the homogenization method presented show good agreement with the heterogeneous simulations

Numerical Simulation and Homogenization of Two-Phase Flow in Heterogeneous Porous Media

This paper is devoted to the homogenization of a coupled system of diffusion-convection equations in a domain with periodic microstructure, modeling the flow and transport of immiscible compressible, such as water-gas, fluids through porous media. The problem is formulated in terms of a nonlinear parabolic equation for the nonwetting phase pressure and a nonlinear degenerate parabolic diffusion-convection equation for the wetting saturation phase with rapidly oscillating porosity function and absolute permeability tensor. We obtain a nonlinear homogenized problem with effective coefficients which are computed via a cell problem. We rigorously justify this homogenization process for the problem by using two-scale convergence. In order to pass to the limit in nonlinear terms, we also obtain compactness results which are nontrivial due to the degeneracy of the system.

Homogenization of Immiscible Compressible Two-Phase Flow in Porous Media: Application to Gas Migration in a Nuclear Waste Repository

A new formulation is presented for the modeling of immiscible compressible two-phase flow in porous media taking into account gravity, capillary effects, and heterogeneity. The formulation is intended for the numerical simulation of multidimensional flows and is fully equivalent to the original equations, contrary to the one introduced in Chavent and Jaffre (Mathematical Models and Finite Elements for Reservoir Simulation, 1986). The main feature of this formulation is the introduction of a global pressure. The resulting equations are written in a fractional flow formulation and lead to a coupled system which consists of a nonlinear parabolic (the global pressure equation) and a nonlinear diffusion–convection one (the saturation equation) which can be efficiently solved numerically. A finite volume method is used to solve the global pressure equation and the saturation equation for the water and gas phase in the context of gas migration through engineered and geological barriers for a deep repository for radioactive waste. Numerical results for the one-dimensional problem are presented. The accuracy of the fully equivalent fractional flow model is demonstrated through comparison with the simplified model already developed in Chavent and Jaffre (Mathematical Models and Finite Elements for Reservoir Simulation, 1986).

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Brahim Amaziane

Papers

Two-phase flow in heterogeneous porous media

Convergence of finite volume schemes for a degenerate convection-diffusion equation arising in flow in porous media

Numerical Simulation and Homogenization of Two-Phase Flow in Heterogeneous Porous Media

Homogenization of Immiscible Compressible Two-Phase Flow in Porous Media: Application to Gas Migration in a Nuclear Waste Repository

Modeling and Numerical Simulations of Immiscible Compressible Two-Phase Flow in Porous Media by the Concept of Global Pressure