Comparison of fast algorithms for estimating large-scale permeabilities of heterogeneous media

1995 ◽  
Vol 19 (2) ◽  
pp. 123-137 ◽  
Author(s):  
J. F. McCarthy
Keyword(s):  
Large Scale ◽  
Heterogeneous Media ◽  
Fast Algorithms

Large-scale analysis of focused ultrasound in heterogeneous media

2010 ◽  
Author(s):  
Junko Uebayashi ◽  
Yoshiaki Tamura ◽  
Yoichiro Matsumoto ◽  
Kullervo Hynynen ◽  
Jacques Souquet
Keyword(s):  
Large Scale ◽  
Focused Ultrasound ◽  
Heterogeneous Media ◽  
Scale Analysis ◽  
Large Scale Analysis

scholarly journals Upscaling Fractured Heterogeneous Media: Permeability and Mass Exchange Coefficient

2005 ◽  
Vol 73 (1) ◽  
pp. 41-46 ◽  
Author(s):  
Moussa Kfoury ◽  
Rachid Ababou ◽  
Benoît Noetinger ◽  
Michel Quintard
Keyword(s):  
Large Scale ◽  
Fluid Transport ◽  
Heterogeneous Media ◽  
Porous Matrix ◽  
Exchange Coefficient ◽  
Flow Equations ◽  
Unit Scale ◽  
Homogenization Methods ◽  
Fracture Distribution ◽  
Equivalent Properties

In order to optimize oil recuperation, to secure waste storage, CO2 sequestration and describe more precisely many environmental problems in the underground, we need to improve some homogenization methods that calculate petrophysical parameters. In this paper, we discuss the upscaling of fluid transport equations in fractured heterogeneous media consisting of the fractures themselves and a heterogeneous porous matrix. Our goal is to estimate precisely the fluid flow parameters like permeability and fracture/matrix exchange coefficient at large scale. Two approaches are possible. The first approach consists in calculating the large-scale equivalent properties in one upscaling step, starting with a single continuum flow model at the local scale. The second approach is to perform upscaling in two sequential steps: first, calculate the equivalent properties at an intermediate scale called the ”unit scale,” and, second, average the flow equations up to the large scale. We have implemented the two approaches and applied them to randomly distributed fractured systems. The results allowed us to obtain valuable information in terms of sizes of representative elementary volume associated to a given fracture distribution.

Fast algorithms for large-scale periodic structures

2004 ◽  
Author(s):  
Wei-Bing Lu ◽  
Tie Jun Cui ◽  
Zhi-Guo Qian ◽  
Xiao Xing Yin ◽  
Wei Hong
Keyword(s):  
Large Scale ◽  
Periodic Structures ◽  
Fast Algorithms

scholarly journals Fast algorithms for large scale conditional 3D prediction

2008 ◽  
Author(s):  
Liefeng Bo ◽  
Cristian Sminchisescu ◽  
Atul Kanaujia ◽  
Dimitris Metaxas
Keyword(s):  
Large Scale ◽  
Fast Algorithms

Characterization of fluid transport properties of reservoirs using induced microseismicity

Geophysics ◽  
2002 ◽  
Vol 67 (1) ◽  
pp. 212-220 ◽  
Author(s):  
Serge A. Shapiro ◽  
Elmar Rothert ◽  
Volker Rath ◽  
Jan Rindschwentner
Keyword(s):  
Large Scale ◽  
Eikonal Equation ◽  
Fluid Transport ◽  
Heterogeneous Media ◽  
Reservoir Characterization ◽  
Homogeneous Medium ◽  
Front Propagation ◽  
Characteristic Size ◽  
Permeability Tensor ◽  
Heterogeneous Rock

We systematically describe an approach to estimate the large‐scale permeability of reservoirs using seismic emission (microseismicity) induced by fluid injection. We call this approach seismicity‐based reservoir characterization (SBRC). A simple variant of the approach is based on the hypothesis that the triggering front of hydraulically‐induced microseismicity propagates like a diffusive process (pore pressure relaxation) in an effective homogeneous anisotropic poroelastic fluid‐saturated medium. The permeability tensor of this effective medium is the permeability tensor upscaled to the characteristic size of the seismically active heterogeneous rock volume. We show that in a homogeneous medium the surface of the seismicity triggering front has the same form as the group‐velocity surface of thelow‐frequency anisotropic, second‐type Biots wave describing kinematic aspects of triggering‐front propagation in a way similar to the eikonal equation for seismic wavefronts. In the case of isotropic heterogeneous media, the inversion for the hydraulic properties of rocks follows from a direct application of this equation. In the case of an anisotropic heterogeneous medium, only the magnitude of a global effective permeability tensor can be mapped in a 3‐D spatial domain. We demonstrate the method on several field examples and also test the eikonal equation‐based inversion.

Transport in Highly Heterogeneous Porous Media: From Direct Simulation to Macro-Scale Two-Equation Models or Mixed Models

2008 ◽  
Vol 3 (1) ◽  
Author(s):  
Debenest Gérald ◽  
Michel Quintard
Keyword(s):  
Porous Media ◽  
Mixed Models ◽  
Large Scale ◽  
Chemical Engineering ◽  
Heterogeneous Media ◽  
Theoretical Models ◽  
Heterogeneous Porous Media ◽  
Petroleum Engineering ◽  
Direct Simulation ◽  
Macro Scale

Flows in highly heterogeneous porous media are found in many practical fields, such as hydrology, petroleum engineering, and chemical engineering. The case of two-region heterogeneous media (fractured media, catalytic beds, etc.) plays a fundamental role. The different questions associated with this specific case are illustrated in this paper for two different kinds of transport: (i) flow of a slightly compressible fluid, (ii) dispersion of a tracer. Many different theoretical models are implemented using COMSOL Multiphysics™. These models correspond to direct simulation and macro-scale or large-scale models such as fully averaged models or mixed models.

Fast algorithms for large-scale periodic structures using subentire domain basis functions

2005 ◽  
Vol 53 (3) ◽  
pp. 1154-1162 ◽  
Author(s):  
Wei Bing Lu ◽  
Tie Jun Cui ◽  
Xiao Xing Yin ◽  
Zhi Guo Qian ◽  
Wei Hong
Keyword(s):  
Large Scale ◽  
Periodic Structures ◽  
Fast Algorithms ◽  
Basis Functions
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