A Numerical Study of the Effects of Wave-Induced Fluid Flow in Porous Media: Linear Solver

In this paper, we present a computational method to simulate wave propagation in porous rocks saturated with Newtonian fluids over a range of frequencies of interest. The method can use a digital representation of a rock sample where distinct material phase and properties at each volume cell are identified and model the dynamic response of the rock to an acoustic excitation mathematically with a coupled equation system: elastic wave equation in solid matrix and viscous wave equation in fluid. The coupled wave equations are solved numerically with a rotated-staggered-grid finite difference scheme. We simulate P-wave propagation through an idealized porous medium of periodically alternating solid and fluid layers where an analytical solution is available and obtain excellent agreements between numerical and analytical solutions. The method models the effect of pore fluid motion on the rock dynamic response more accurately with a linearized Navier-Stokes equation than with the viscoelastic model of the generalized Maxwell body, a low frequency approximation commonly used to overcome the difficulty of modeling frequency-dependent fluid shear modulus in time domain.