Difficulties arising from different definitions of tortuosity for wave propagation in saturated poroelastic media models

Abstract

The multiple definitions of permeability and tortuosity employed by investigators modifying the basic equations of dynamic poroelasticity pose a problem as some resulting analyses produce results conflicting with those of other investigators. When the same words are used to describe different definitions of different concepts, the problem is compounded. These problems were highlighted in recent applications of acceleration wave analyses of dynamic poroelasticity. Wilmanski [40] and Coussy [14] applied acceleration wave analysis to their own systems of dynamic poroelastic equations and found contradictory results. In one case the wave speed depends upon tortuosity and in the other case a dependence upon permeability (and tortuosity) was not allowed. This means that acceleration waves in the Wilmanski [40] analysis cannot exhibit dispersion at lower frequencies. Harmonic wave analyses applied to the same systems of dynamic poroelastic equations predict a dependence of wave speed upon permeability. The acceleration wave analysis of a system of dynamic poroelastic equations is dependent upon the definitions of tortuosity used by the investigators. Wilmanski [40] and Coussy [14] each used their own definition of tortuosity.