Pore-Scale Simulation Of Experimentally Realizable, Oscillatory Flow In Porous Rock

Abstract

We report new simulations of oscillating flow in porous rock. Our goal is to better understand the frequency dependence of pore-scale fluid motion, which should ultimately help us to interpret attenuation and electroseismic measurements. We use a lattice gas cellular automaton (Rothman and Zaleski, 1997) to perform the calculations in a pore space geometry measured from Fontainebleau sandstone by X-ray microtomography (Spanne et al., 1994; Auzerais et al., 1996). We chose this method because it is fast and efficient in the complex geometry of the porous rock. We show that the Biot critical frequency (Biot, 1956) is accessible to simulation, and we perform simulations at a range of frequencies around the critical frequency. In addition, we show that the dynamical properties of the lattice gas fluid can be mapped onto reasonable real fluids. As the frequency varies through the critical range, we observe qualitative and quantitative changes in the amplitude and phase of fluid velocity distributions. We also report preliminary calculations of the local viscous dissipation, which should provide a means to compare our simulations with existing theories of attenuation (e.g., Johnston et al., 1979; Dvorkin and Nur, 1993; Akbar et al., 1994).