A Level Set Method for the Inverse Problem of Wave Equation in the Fluid-Saturated Porous Media

2009 ◽  
Vol 6 (4) ◽  
pp. 793-803
Author(s):  
Ying He ◽  
Bo Han
Keyword(s):  
Inverse Problem ◽  
Porous Media ◽  
Wave Equation ◽  
Level Set Method ◽  
Level Set ◽  
Saturated Porous Media ◽  
Fluid Saturated Porous Media

A Multi-Scale and Level Set Algorithm for the Inverse Problem of Wave Equation

2013 ◽  
Vol 275-277 ◽  
pp. 413-416
Author(s):  
Ying He ◽  
Chun Yan He
Keyword(s):  
Porous Media ◽  
Elastic Wave ◽  
Level Set ◽  
Wave Equations ◽  
Biot Theory ◽  
Saturated Porous Media ◽  
Parameter Recovery ◽  
Multi Scale ◽  
Elastic Wave Equations ◽  
Fluid Saturated Porous Media

In this paper, we construct the multi-scale and level set algorithm of the parameter recovery for the elastic wave equations in the fluid-saturated porous media. Firstly, based on the Biot theory, we apply the multi-scale method to simulate the propagation of 2-D elastic wave in fluid-saturated porous media. Secondly, the level set method is introduced to the general parameter estimation problem.

Seismic wave equation formulated by generalized viscoelasticity in fluid-saturated porous media

Geophysics ◽  
2021 ◽  
pp. 1-37
Author(s):  
Hanming Gu ◽  
Jun Ni ◽  
Yanghua Wang
Keyword(s):  
Porous Media ◽  
Wave Equation ◽  
Generalized Equation ◽  
P Wave ◽  
Solid Skeleton ◽  
Saturated Porous Media ◽  
Viscoelastic Parameter ◽  
Viscoelastic Wave Equation ◽  
Viscoelastic Wave ◽  
Fluid Saturated Porous Media

Biot’s theory of poroelasticity describes seismic waves propagating through fluid-saturated porous media, so-called two-phase media. The classic Biot’s theory of poroelasticity considers the wave dissipation mechanism being the friction of relative motion between the fluid in the pores and the solid rock skeleton. However, within the seismic frequency band, the friction has a major influence only on the slow P-wave and has an insignificant influence on the fast P-wave. In order to represent the intrinsic viscoelasticity of the solid skeleton, we incorporate a generalized viscoelastic wave equation into Biot’s theory for the fluid-saturated porous media. The generalized equation which unifies the pure elastic and viscoelastic cases is constituted by a single viscoelastic parameter, presented as the fractional order of the wavefield derivative in the compact form of the wave equation. The generalized equation that includes the viscoelasticity appropriately describes the dissipation characteristics of the fast P-wave. Plane-wave analysis and numerical solutions of the proposed wave equation reveal that (1) the viscoelasticity in the solid skeleton causes the energy attenuation on the fast P-wave and the slow P-wave at the same order of magnitude, and (2) the generalized viscoelastic wave equation effectively describes the dissipation effect of the waves propagating through the fluid-saturated porous media.

Semi-analytical finite element method for simulating chemical dissolution-front instability problems in fluid-saturated porous media

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Chongbin Zhao ◽  
B.E. Hobbs ◽  
Alison Ord
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Porous Media ◽  
Chemical Dissolution ◽  
Saturated Porous Media ◽  
Content Type ◽  
Front Instability ◽  
Fluid Saturated Porous Media ◽  
Dissolution Front ◽  
Element Method

PurposeThe objective of this paper is to develop a semi-analytical finite element method for solving chemical dissolution-front instability problems in fluid-saturated porous media.Design/methodology/approachThe porosity, horizontal and vertical components of the pore-fluid velocity and solute concentration are selected as four fundamental unknown variables for describing chemical dissolution-front instability problems in fluid-saturated porous media. To avoid the use of numerical integration, analytical solutions for the property matrices of a rectangular element are precisely derived in a purely mathematical manner. This means that the proposed finite element method is a kind of semi-analytical method. The column pivot element solver is used to solve the resulting finite element equations of the chemical dissolution-front instability problem.FindingsThe direct use of horizontal and vertical components of the pore-fluid velocity as fundamental unknown variables can improve the accuracy of the related numerical solution. The column pivot element solver is useful for solving the finite element equations of a chemical dissolution-front instability problem. The proposed semi-analytical finite element method can produce highly accurate numerical solutions for simulating chemical dissolution-front instability problems in fluid-saturated porous media.Originality/valueAnalytical solutions for the property matrices of a rectangular element are precisely derived for solving chemical dissolution-front instability problems in fluid-saturated porous media. The proposed semi-analytical finite element method provides a useful way for understanding the underlying dynamic mechanisms of the washing land method involved in the contaminated land remediation.

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