A wavelet finite-difference method for numerical simulation of wave propagation in fluid-saturated porous media

2008 ◽  
Vol 29 (11) ◽  
pp. 1495-1504 ◽  
Author(s):  
Ying He ◽  
Bo Han
Keyword(s):  
Numerical Simulation ◽  
Porous Media ◽  
Wave Propagation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Saturated Porous Media ◽  
Fluid Saturated Porous Media

Wave propagation in heterogeneous, porous media: A velocity‐stress, finite‐difference method

Geophysics ◽  
1995 ◽  
Vol 60 (2) ◽  
pp. 327-340 ◽  
Author(s):  
N. Dai ◽  
A. Vafidis ◽  
E. R. Kanasewich
Keyword(s):  
Porous Media ◽  
Wave Propagation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Hyperbolic System ◽  
Particle Velocity ◽  
Difference Method ◽  
Numerical Solutions ◽  
Second Order ◽  
P Wave

A particle velocity‐stress, finite‐difference method is developed for the simulation of wave propagation in 2-D heterogeneous poroelastic media. Instead of the prevailing second‐order differential equations, we consider a first‐order hyperbolic system that is equivalent to Biot’s equations. The vector of unknowns in this system consists of the solid and fluid particle velocity components, the solid stress components, and the fluid pressure. A MacCormack finite‐difference scheme that is fourth‐order accurate in space and second‐order accurate in time forms the basis of the numerical solutions for Biot’s hyperbolic system. An original analytic solution for a P‐wave line source in a uniform poroelastic medium is derived for the purposes of source implementation and algorithm testing. In simulations with a two‐layer model, additional “slow” compressional incident, transmitted, and reflected phases are recorded when the damping coefficient is small. This “slow” compressional wave is highly attenuated in porous media saturated by a viscous fluid. From the simulation we also verified that the attenuation mechanism introduced in Biot’s theory is of secondary importance for “fast” compressional and rotational waves. The existence of seismically observable differences caused by the presence of pores has been examined through synthetic experiments that indicate that amplitude variation with offset may be observed on receivers and could be diagnostic of the matrix and fluid parameters. This method was applied in simulating seismic wave propagation over an expanded steam‐heated zone in Cold Lake, Alberta in an area of enhanced oil recovery (EOR) processing. The results indicate that a seismic surface survey can be used to monitor thermal fronts.

A Fractional Generalised Finite Difference Method to Linear Porous Media Dynamics

2016 ◽  
Vol 846 ◽  
pp. 403-408 ◽  
Author(s):  
Y.P. Zhang ◽  
D.M. Pedroso ◽  
L. Li
Keyword(s):  
Porous Media ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Theoretical Background ◽  
Saturated Porous Media ◽  
Mesh Free ◽  
Mesh Free Method ◽  
Dynamics Simulations ◽  
Interpolation Functions

The generalised finite difference method (GFDM) is a mesh-free method for solving partial differential equations (PDEs) in non-structured grids. Due to its strong theoretical background and simplicity, hence efficiency, it has been introduced to handle interesting and sophisticate engineering problems. However, the GFDM has not been applied to problems associated to dynamics of porous media yet. In these problems, the strong coupling between solid displacements and liquid pressures may cause large numerical oscillations if equal order interpolation functions are used for both variables. Nevertheless, some fractional steps techniques can be introduced in order to minimise these problems. In this contribution, a fractional steps scheme is developed and applied to the GFDM in order to model fully saturated porous media dynamics. Simulations of 1D and 2D wave propagation are performed in order to reveal the advantages, drawbacks and capabilities of the proposed method.

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